Describe the Analysis
Main goal:
?
Describe the Loan
Mortgage type:
?
Describe the Rate Adjustment Rules
Describe the Costs Paid at Closing
Describe the Prepayment Strategy
Number of prepayments per year:
?
Enter Tax and Insurance Info
Summary Report
To create a report, enter data into the Mortgage Calculator
and click the Calculate button.
Frequently-Asked Questions
Instructions: To find the answer to a frequently-asked
question, simply click on the question.
See also:
Mortgage Case Studies
How do I use the mortgage
calculator?
The Mortgage Mavin calculator is accessible
from the Mortgage calculator link at the top of every
Mortgage Mavin web page. Working with the calculator
involves a simple, three-step process:
- Describe the analysis. Choose your main goal and
select options - produce an amortization schedule,
include taxes and insurance,
assess the prepayment effects, and compute tax savings.
- Enter data. Based on the options you select, the
calculator will prompt you for
inputs (mortgage type, interest rate, loan amount, loan term, etc.)
needed to conduct the analysis.
- Report results. After you provide the data
requested, click the
Calculate button. The calculator displays a
summary report that clearly presents key findings, based on
data you entered.
Which goal should I choose
for my analysis?
The mortgage calculator gives you a choice of six different
goals. Here is what you get with each option.
- Find monthly mortgage. Select this goal when you are
only interested in the monthly mortgage payment. Based on your input
(loan amount, loan term, interest rate), the calculator will report
monthly payment (principal and interest). If you wish, you can
include the effect of other factors (e.g., property tax, hazard
insurance, mortgage insurance, and prepayments) on the monthly payment.
And finally, you can create an amortization schedule that tracks
the amount paid and the amount due over the life of the mortgage.
- Find total mortgage cost. This option provides
everything that you get with the monthly mortgage option (described
above). In addition, you get more detail on mortgage cost (e.g.,
closing costs, points, settlement fees); and you can evaluate the
effect of tax deductions for points and interest.
- Find savings from prepayment. Use this option to
understand prepayment effects - how much quicker you can pay off your
mortgage and how much money you can save over the life of your
mortgage. In addition, this option provides
everything that you get with the monthly mortgage option (described
above).
- Compare two mortgages. This option allows you to
easily compare two mortgages - interest expense, settlement costs,
private mortgage insurance, loan duration, etc. The final report
shows total cost over the lifetime of each mortgage, with and without
tax deductions. An amortization report allows you to compare total
cost for each mortgage at any point in time. And finally, this
option computes monthly mortgage payments for each mortgage.
- Evaluate refinancing plan. This option allows
you to easily assess the costs and benefits of refinancing your
current mortgage. It compares loan duration and cost, with and
without refinancing. And it shows how long it will take for
refinancing savings to pay for refinancing costs.
- Display amortization table. This option allows
you to easily generate an amortization table (aka, amortization
chart, amortization schedule) for ten types of mortgage.
The amortization table shows how much of each mortgage payment goes
toward principal, how much goes toward interest, and
the amount required to retire the loan in each payment period.
Additionally, for each payment period, this amortization table shows
the total loan cost (principal, interest, closing costs, etc.)
if the loan is paid off in that payment period.
What kinds of problems
can the mortgage calculator handle?
This home mortgage calculator is versatile. Use it to
answer common questions about home loans, such as:
What kinds of mortgages can the
mortgage calculator handle?
This mortgage calculator works with many kinds of mortgages - four
kinds of
fixed-rate mortgage and six kinds of
adjustable-rate mortgage, as shown in the table below.
To specify the mortgage that you want to work with, select an entry from the "Mortgage Type" dropdown box. The current entry is "Fixed-Rate Mortgage", so the mortgage calculator will generate an amortization table for a Fixed-Rate Mortgage.
What interest rate does the
calculator use for adjustable-rate mortgages?
With
adjustable-rate mortgages,
interest rates usually change over time. Even though we can't know
the direction and magnitude of future changes, we do know the
maximum rate in any payment period; since the maximum rate is defined
by a periodic or lifetime
rate cap.
Every time a new rate is called for, the mortgage calculator
assumes a worst-case scenario; that is, the calculator assumes that
the new rate is equal to the maximum rate.
Note: By assuming a worst-case scenario for
every payment period, the mortgage calculator will probably
overestimate the true cost of an adjustable-rate mortgage,
but the home buyer will never be surprised by a larger-than-expected bill.
What are the meanings of the various
financial terms used by the mortgage calculator?
For help with any financial term used by the mortgage
calculator, click the
Help Icon
,
? ,
to its right.
If you need additional help, check the Mortgage Mavin
mortgage dictionary. To access the dictionary,
click the "Mortgage dictionary" hyperlink that appears at the top of every
Mortgage Mavin web page.
What is the history of the mortgage
calculator?
For most of the 20th century, home buyers, lending institutions, and real
estate professionals relied
on dense, hard-to-read tables to answer simple questions about mortgage
properties (payment amount, loan duration, interest expense, etc.).
Obtaining information was tedious, and human error was rampant.
Toward the end of the century, handheld financial calculators became the
tool of choice. This was an improvement, but there were still problems.
Using the calculators required training, interpreting the results
required experience, and there was a price. Handheld calculators
are not free.
Today, in the 21st century, everything is better. No more
hard-to-read tables.
No need for costly, hard-to-use handheld calculators. Mortgage Mavin's
online mortgage calculator provides the answers you need - fast, easy,
and free. The information you need is just a mouse click away.
Sample Problems
This section shows how to use the
mortgage calculator to answer a common mortgage question.
For more sample problems, see the Mortgage Mavin
case studies.
Problem
Bob needs a mortgage loan of $250,000. He is considering a
fixed-rate balloon loan. Mortgage payments are based on a 30-year loan term, with
a starting interest rate of 6.5%. The
balloon note term is 5 years. This means that Bob will need to pay off the
unpaid loan balance in full, after 5 years.
In 5 years, when Bob pays off the loan, what will the balance be?
Solution:
As part of its summary report, the mortgage calculator generates an
amortization table, which shows the principal and interest paid in every payment
period. However, the Mortgage Mavin calculator provides some "extra" information
when the main goal is "Find monthly mortgage". In particular, it shows the remaining
balance after every payment period. Therefore, to solve this
problem, you just need to produce an amortization table and check the balance
at the 5-year mark. Here's how.
First, Choose "Find monthly mortgage" from the Main Goal
dropdown box. And in the Options section, check "Show amortization schedule". This
will ensure that the summary report generates an amortization schedule that shows
the loan balance after 5 years (i.e., after month 60).
The calculator will prompt you for the data it needs. Provide the data,
as shown below.
Describe the Analysis
Main goal:
Describe the Loan
Mortgage type:
Months before note must be paid:
After you press the Calculate button, the mortgage calculator
generates a summary report that includes an amortization table. The amortization
table shows the principal due after each payment period. By examining month 60
of the amortization table, you see that the remaining balance after 5 years
(60 months) is $234,026.75. Thus, the
balloon payment
due after 5 years (60 months) is $234,026.75.
Problem
Ted needs a mortgage loan of $200,000. He has chosen a 30-year
fixed-rate loan, with a starting interest rate of 6.5%.
What will Ted's monthly payment be for principal and interest?
Solution:
First, Choose "Find monthly mortgage" from the Main Goal
dropdown box of the Mortgage Mavin calculator. And in the Options section,
check "Include amortization schedule".
Based on these settings, the calculator will prompt you for the data it needs.
Provide the data, as shown below.
Describe the Analysis
Main goal:
Describe the Loan
Mortgage type:
After you press the Calculate button, the mortgage calculator
generates a summary report, which shows that Ted will pay $1264.15 each
month for principal and interest.
In addition, the amortization table shows the contribution of principal
and interest in each payment period. For example, in the first payment period,
Ted pays $180.82 toward principal and $1,083.33 toward interest.
Problem
Alice is buying a new home for $220,000. She will make a down payment of
$20,000 and get a $200,000
fixed-rate mortgage. The mortgage is a 30-year loan with an 8 percent
interest rate. At closing, she will pay one
discount point and
$3,000 in other costs.
Suppose that the fair market value of Alice's home is $220,000, and the annual
cost of private mortgage insurance is $1,800 per year.
What will be the total mortgage cost over the 30-year life of the loan?
Suppose Alice sells her home after 10 years. What will be the total cost
of the mortgage after 10 years?
Solution:
As part of its summary report, the Total Cost Mortgage Calculator generates an
amortization table. Most amortization tables show just the principal and interest
paid in every payment period. However, the amortization table produced by this
calculator also shows the total cost of
the mortgage at every payment period. Therefore, to solve this
problem, you just need to produce an amortization table and check the total cost
after 10 years and after 30 years. Here's how.
First, choose "Find total mortgage cost" from the Main Goal
dropdown box. And in the Options section, check "Show amortization schedule" and
check "Include mortgage insurance". This tells the calculator to produce an
amortization table that accounts for private mortgage insurance as part of the
total cost.
Given these settings, the calculator will prompt you for the data it needs.
Provide the data, as shown below.
Describe the Analysis
Main goal:
Describe the Loan
Mortgage type:
Describe the Costs Paid at Closing
Other costs and fees ($):
Enter Insurance Info
Annual mortgage insurance ($):
Appraised value of home ($):
After you press the Calculate button, the mortgage calculator
generates a summary report that includes an amortization table. The
amortization table shows that Alice's total mortgage cost over the 30-year
life of this fixed-rate mortgage will be $571,148.20. The amortization table
also shows the
total cost after 10 years. If Alice sells her home (and pays off
the mortgage) after 10 years, her total cost will be $394,402.23.
Problem
Betty is buying a new home for $220,000. She will make a down payment of
$20,000 and get a $200,000
biweekly fixed-rate mortgage. The mortgage is a 30-year loan with an
8 percent interest rate. At closing, she will pay one
discount point and
$3,000 in other costs.
What will be the total mortgage cost over the 30-year life of the loan?
Suppose Betty sells her home after 10 years. What will be the total cost
of the mortgage after 10 years?
Solution:
As part of its summary report, the Total Cost Mortgage Calculator generates an
amortization table. Most amortization tables show just the principal and interest
paid in every payment period. However, the amortization table produced by this
calculator also shows the total cost of
the mortgage at every payment period. Therefore, to solve this
problem, you just need to produce an amortization table and check the total cost
after 10 years and after 30 years. Here's how.
First, Choose "Find total mortgage cost" from the Main Goal
dropdown box. And in the Options section, check "Show amortization schedule" and
check "Include mortgage insurance". This tells the calculator to produce an
amortization table that accounts for private mortgage insurance as part of the
total cost.
Given these settings, the calculator will prompt you for the data it needs.
Provide the data, as shown below.
Describe the Analysis
Main goal:
Describe the Loan
Mortgage type:
Describe the Costs Paid at Closing
Other costs and fees ($):
Enter Insurance Info
Annual mortgage insurance ($):
Appraised value of home ($):
After you press the Calculate button, the mortgage calculator
generates a summary report that includes an amortization table. The
amortization table shows that Betty's total mortgage cost over the 30-year
life of this biweekly fixed-rate loan will be $570,876.06.
The amortization table also shows the
total cost after 10 years. If Betty sells her home (and pays off
the mortgage) after 10 years, her total cost will be $394,321.43.
Problem
Carla is buying a new home for $220,000. She will make a down payment of
$20,000 and get a $200,000 fixed-rate
balloon loan. Monthly mortgage payments are based
on a 30-year loan with an 8 percent interest rate.
The balloon term
is 60 months. This means that Carla will have
to pay off the loan balance in 60 months (5 years).
At closing, Carla will pay one
discount point and
$3,000 in other costs.
After 5 years, when Carla pays off the loan, what will be the loan balance?
What will be the total cost of the mortgage?
Solution:
As part of its summary report, the Total Cost Mortgage Calculator generates
many outputs, including an amortization table. In addition to the principal and
interest paid in every payment period, this amortization table shows the total cost of
the mortgage and the loan balance in every payment period. Therefore, to solve this
problem, you just need to produce an amortization table and check the total cost
and loan balance after 5 years. Here's how.
First, Choose "Find total mortgage cost" from the Main Goal
dropdown box. And in the Options section, check "Show amortization schedule".
Given these settings, the calculator will prompt you for the data it needs.
Provide the data, as shown below.
Describe the Analysis
Main goal:
Describe the Loan
Mortgage type:
Months before note must be paid:
Describe the Costs Paid at Closing
Other costs and fees ($):
After you press the Calculate button, the mortgage calculator
generates a summary report that includes an amortization table. The
amortization table shows that the balance remaining is $190,138.92, and the total
cost of the mortgage is $303,191.32.
The mortgage calculator also produces a table that shows the
components of total mortgage cost for this fixed-rate balloon loan.
Relevant portions of that table appear below.
| Principal due: |
$190,138.92 |
| Principal paid: |
$9,861.08 |
| Total interest expense: |
$78,191.32 |
| Down payment: |
$20,000 |
| Points: |
$2,000 |
| Other loan costs: |
$3,000 |
| Total mortgage cost: |
$303,191.32 |
Problem
David is buying a new home for $220,000. He will make a down payment of
$20,000 and get a $200,000 fixed-rate
interest-only loan, with an 8 percent interest rate.
At closing, David will pay one
discount point and
$3,000 in other costs. The mortgage requires David to pay off the loan balance
in 60 months (5 years).
After 5 years, when David pays off the loan, what will be the loan balance?
What will be the total cost of the mortgage?
Solution:
As part of its summary report, the Total Cost Mortgage Calculator generates
many outputs, including an amortization table. In addition to the principal and
interest paid in every payment period, this amortization table shows the total cost of
the mortgage and the loan balance in every payment period. Therefore, to solve this
problem, you just need to produce an amortization table and check the total cost
and loan balance after 5 years. Here's how.
First, Choose "Find total mortgage cost" from the Main Goal
dropdown box. And in the Options section, check "Show amortization schedule".
Given these settings, the calculator will prompt you for the data it needs.
Provide the data, as shown below.
Describe the Analysis
Main goal:
Describe the Loan
Mortgage type:
Months before note must be paid:
Describe the Costs Paid at Closing
Other costs and fees ($):
After you press the Calculate button, the interest-only mortgage calculator
generates a summary report that includes an amortization table. The
amortization table shows that the balance remaining is $200,000, and the total
cost of the mortgage is $304,999.80.
The mortgage calculator also produces a table that shows the
components of total mortgage cost for this fixed-rate interest-only loan.
Relevant portions of that table appear below.
| Principal due: |
$200,000 |
| Principal paid: |
$0 |
| Total interest expense: |
$79,999.80 |
| Down payment: |
$20,000 |
| Points: |
$2,000 |
| Other loan costs: |
$3,000 |
| Total mortgage cost: |
$304,999.80 |
Problem
Esther is buying a new home for $220,000. She will make a down payment of
$20,000 and get a $200,000
adjustable-rate mortgage (ARM).
At closing, Esther will pay one
discount point and
$3,000 in other costs. The loan details are described below.
| Mortgage type: |
Adjustable-rate mortgage |
First rate adjustment at: |
60 months |
| Starting interest rate: |
6 percent |
Periodic rate cap: |
2 percent |
| Loan amount: |
$200,000 |
Maximum lifetime rate cap: |
12 percent |
| Loan term: |
30 years |
Months between adjustments: |
12 months |
What will be the total mortgage cost over the 30-year life of the loan?
Suppose Esther sells her home after 10 years. What will be the total cost
of the mortgage after 10 years?
Solution:
As part of its summary report, the Total Cost Mortgage Calculator generates an
amortization table. Most amortization tables show just the principal and interest
paid in every payment period. However, the amortization table produced by this
calculator also shows the total cost of
the mortgage at every payment period. Therefore, to solve this
problem, you just need to produce an amortization table and check the total cost
after 10 years and after 30 years. Here's how.
First, Choose "Find total mortgage cost" from the Main Goal
dropdown box. And in the Options section, check "Show amortization schedule".
Given these settings, the calculator will prompt you for the data it needs.
Provide the data, as shown below.
Describe the Analysis
Main goal:
Describe the Loan
Mortgage type:
Describe the Rate Adjustment Rules
Months before first rate adjustment:
Maximum lifetime interest rate (%):
Months between rate adjustments:
Describe the Costs Paid at Closing
Other costs and fees ($):
After you press the Calculate button, the mortgage calculator
generates a summary report that includes an amortization table. The
amortization table shows that Esther's total mortgage cost over the 30-year
life of the loan will be $733,741.78. The amortization table also shows the
total cost after 10 years. If Esther sells her home (and pays off
the mortgage) after 10 years, her total cost will be $431,718.74.
Note: This analysis assumes that the adjustable-rate mortgage
"adjusts" to its maximum interest rate of 12 percent - a worst-case scenario.
This might overstate the true lifetime cost of the adjustable-rate mortgage.
An alternative analysis would be to employ a best-guess scenario; i.e., guess
the average interest rate over the life of the adjustable-rate mortgage and assume
that the maximum interest rate equals the hypothesized average interest
rate. For more info on this topic, see
Adjustable-Rate Mortgages:
Dealing With Uncertainty.
Problem
Evelyn is buying a new home for $220,000. To pay for the home, she will
make a down payment of $20,000 and get a $200,000
convertible ARM. At closing, she will pay one
discount point and
$3,000 in other costs. The loan details are described below.
| Mortgage type: |
Convertible ARM |
Duration of adjustable rate: |
60 months |
| Starting interest rate: |
6 percent |
Periodic rate cap: |
2 percent |
| Loan amount: |
$200,000 |
Lifetime rate cap: |
12 percent |
| Loan term: |
30 years |
Between adjustments: |
12 months |
|
|
Final fixed interest rate: |
8 percent |
|
|
Cost to convert: |
$1,000 |
Suppose that the fair market value of Evelyn's home is $220,000, and the annual
cost of private mortgage insurance is $1,800 per year. Suppose also that
Evelyn converts to a fixed interest rate of 8 percent after 60 months.
What will be the total mortgage cost over the 30-year life of the loan?
Suppose Evelyn sells her home after 10 years. What will be the total cost
of the mortgage after 10 years?
Solution:
As part of its summary report, the Total Cost Mortgage Calculator generates an
amortization table. Most amortization tables show just the principal and interest
paid in every payment period. However, the amortization table produced by this
calculator also shows the total cost of
the mortgage at every payment period. Therefore, to solve this
problem, you just need to produce an amortization table and check the total cost
after 10 years and after 30 years. Here's how.
First, Choose "Find total mortgage cost" from the Main Goal
dropdown box. And in the Options section, check "Show amortization schedule" and
check "Include mortgage insurance". This tells the calculator to produce an
amortization table that accounts for private mortgage insurance as part of the
total cost..
Given these settings, the calculator will prompt you for the data it needs.
Provide the data, as shown below.
Describe the Analysis
Main goal:
Describe the Loan
Mortgage type:
Describe the Rate Adjustment Rules
Maximum lifetime interest rate (%):
Months between rate adjustments:
Ending interest rate (%):
Months before fixed rate begins:
Describe the Costs Paid at Closing
Other costs and fees ($):
Enter Insurance Info
Annual mortgage insurance ($):
Appraised value of home ($):
After you press the Calculate button, the mortgage calculator
generates a summary report that includes an amortization table. The
amortization table shows that Mary's total mortgage cost over the 30-year
life of this convertible ARM will be $601,179.54. The amortization table
also shows the
total cost after 10 years. If Mary sells her home (and pays off
the mortgage) after 10 years, her total cost will be $420,353.08.
Problem
Felix is buying a new home for $220,000. He will make a down payment of
$20,000 and get a $200,000
two-step mortgage. The mortgage is a 30-year loan with a starting interest
rate of 6 percent. At closing, he will pay one
discount point and
$3,000 in other costs. The remaining loan details are shown below.
| Mortgage type: |
Two-step mortgage |
Months before rate adjustment: |
60 months |
| Starting interest rate: |
6 percent |
Ending interest rate: |
8 percent |
| Loan amount: |
$200,000 |
|
|
| Loan term: |
30 years |
|
|
What will be the total mortgage cost over the 30-year life of the loan?
Suppose Felix sells his home after 10 years. What will be the total cost
of the mortgage after 10 years?
Solution:
As part of its summary report, the Total Cost Mortgage Calculator generates an
amortization table. Most amortization tables show just the principal and interest
paid in every payment period. However, the amortization table produced by this
calculator also shows the total cost of
the mortgage at every payment period. Therefore, to solve this
problem, you just need to produce an amortization table and check the total cost
after 10 years and after 30 years. Here's how.
First, Choose "Find total mortgage cost" from the Main Goal
dropdown box. And in the Options section, check "Show amortization schedule".
Given these settings, the calculator will prompt you for the data it needs.
Provide the data, as shown below.
Describe the Analysis
Main goal:
Describe the Loan
Mortgage type:
Describe the Rate Adjustment Rules
Months before rate adjustment:
Ending interest rate (%):
Describe the Costs Paid at Closing
Other costs and fees ($):
After you press the Calculate button, the mortgage calculator
generates a summary report that includes an amortization table. The
amortization table shows that Felix's total mortgage cost over the 30-year
life of this two-step mortgage will be $527,865.67. The amortization table also
shows the total cost after 10 years. If Felix sells his home (and pays off
the mortgage) after 10 years, his total cost will be $354,860.58.
Problem
George is buying a new home for $220,000. He will make a down payment of
$20,000 and get a $200,000
adjustable-rate balloon loan. The mortgage is a 30-year loan with a
starting interest rate of 6 percent. The loan details are described below.
| Mortgage type: |
Balloon ARM |
Months before first rate adjustment: |
12 months |
| Starting interest rate: |
6 percent |
Periodic rate cap: |
2 percent |
| Loan amount: |
$200,000 |
Maximum interest rate: |
12 percent |
| Loan term: |
30 years |
Months between adjustments: |
12 months |
| Months before note must be paid: |
60 months |
|
|
At closing, George will pay one
discount point and
$3,000 in other costs.
After 5 years, when George pays off the loan, what will be the loan balance?
What will be the total cost of the mortgage?
Solution:
As part of its summary report, the Total Cost Mortgage Calculator generates
many outputs, including an amortization table. In addition to the principal and
interest paid in every payment period, this amortization table shows the total cost of
the mortgage and the loan balance in every payment period. Therefore, to solve this
problem, you just need to produce an amortization table and check the total cost
and loan balance after 5 years (60 months). Here's how.
First, Choose "Find total mortgage cost" from the Main Goal
dropdown box. And in the Options section, check "Show amortization schedule".
Given these settings, the calculator will prompt you for the data it needs.
Provide the data, as shown below.
Describe the Analysis
Main goal:
Describe the Loan
Mortgage type:
Months before note must be paid:
Describe the Rate Adjustment Rules
Months before first rate adjustment:
Maximum lifetime interest rate (%):
Months between rate adjustments:
Describe the Costs Paid at Closing
Other costs and fees ($):
After you press the Calculate button, the mortgage calculator
generates a summary report that includes an amortization table. The
amortization table shows that the balance remaining is $192,224.29, and the total
cost of the mortgage is $315,901.13.
The mortgage calculator also produces a table that shows the
components of total mortgage cost for this adjustable-rate balloon loan.
Relevant portions of that table appear below.
| Principal due: |
$192,224.29 |
| Principal paid: |
$7,775.71 |
| Total interest expense: |
$93,601.13 |
| Down payment: |
$20,000 |
| Points: |
$2,000 |
| Other loan costs: |
$3,000 |
| Total mortgage cost: |
$315,901.13 |
Note: This analysis assumes that the adjustable-rate mortgage
"adjusts" to its maximum interest rate of 12 percent - a worst-case scenario.
This might overstate the true lifetime cost of the adjustable-rate mortgage.
An alternative analysis would be to employ a best-guess scenario; i.e., guess
the average interest rate over the 5-year life of this adjustable-rate
balloon mortgage and assume
that the maximum interest rate equals the hypothesized average interest
rate. For more info on this topic, see
Adjustable-Rate Mortgages:
Dealing With Uncertainty.
Problem
Herb is buying a new home for $220,000. He will make a down payment of
$20,000 and get a $200,000
adjustable-rate interest-only mortgage, with a
starting interest rate of 6 percent. The loan details are described below.
| Mortgage type: |
Interest-Only ARM |
Months before first rate adjustment: |
12 months |
| Starting interest rate: |
6 percent |
Periodic rate cap: |
2 percent |
| Loan amount: |
$200,000 |
Maximum interest rate: |
12 percent |
| Months before note must be paid: |
60 months |
Months between adjustments: |
12 months |
At closing, Herb will pay one
discount point and
$3,000 in other costs.
After 5 years, when Herb pays off the loan, what will be the loan balance?
What will be the total cost of the mortgage?
Solution:
As part of its summary report, the Total Cost Mortgage Calculator generates
many outputs, including an amortization table. In addition to the principal and
interest paid in every payment period, this amortization table shows the total cost of
the mortgage and the loan balance in every payment period. Therefore, to solve this
problem, you just need to produce an amortization table and check the total cost
and loan balance after 5 years (60 months). Here's how.
First, Choose "Find total mortgage cost" from the Main Goal
dropdown box. And in the Options section, check "Show amortization schedule".
Given these settings, the calculator will prompt you for the data it needs.
Provide the data, as shown below.
Describe the Analysis
Main goal:
Describe the Loan
Mortgage type:
Months before note must be paid:
Describe the Rate Adjustment Rules
Months before first rate adjustment:
Maximum lifetime interest rate (%):
Months between rate adjustments:
Describe the Costs Paid at Closing
Other costs and fees ($):
After you press the Calculate button, the mortgage calculator
generates a summary report that includes an amortization table. The
amortization table shows that the balance remaining is $200,000, and the total
cost of the mortgage is $321,000.
The mortgage calculator also produces a table that shows the
components of total mortgage cost for this adjustable-rate interest-only mortgage.
Relevant portions of that table appear below.
| Principal due: |
$200,000 |
| Principal paid: |
$0 |
| Total interest expense: |
$96,000,000 |
| Down payment: |
$20,000 |
| Points: |
$2,000 |
| Other loan costs: |
$3,000 |
| Total mortgage cost: |
$321,000 |
Note: This analysis assumes that the adjustable-rate mortgage
"adjusts" to its maximum interest rate of 12 percent - a worst-case scenario.
This might overstate the true lifetime cost of the adjustable-rate mortgage.
An alternative analysis would be to employ a best-guess scenario; i.e., guess
the average interest rate over the 5-year life of this adjustable-rate
interest-only mortgage and assume
that the maximum interest rate equals the hypothesized average interest
rate. For more info on this topic, see
Adjustable-Rate Mortgages:
Dealing With Uncertainty.
Problem
Irving is buying a new home for $220,000. To pay for the home, he will
make a down payment of $20,000 and get a $200,000
graduated payment loan. The starting interest rate for this loan is
6 percent. Every 12 months, the interest increases by 1 percentage point,
until the interest rate reaches 9 percent. The loan details are described below.
| Mortgage type: |
Graduated payment loan |
Number of rate adjustments: |
3 |
| Starting interest rate: |
6 percent |
Months between adjustments: |
12 |
| Loan amount: |
$200,000 |
Ending interest rate: |
9 percent |
| Loan term: |
30 years |
|
|
At closing, Irving will pay one
discount point and
$3,000 in other costs.
Suppose that the fair market value of Irving's home is $220,000, and the annual
cost of private mortgage insurance (PMI) is $1,800 per year.
What will be the total mortgage cost over the 30-year life of the loan?
Suppose Irving sells his home after 10 years. What will be the total cost
of the mortgage after 10 years?
Solution:
As part of its summary report, the Total Cost Mortgage Calculator generates an
amortization table, which shows the principal and interest paid in every payment
period. However, unlike typical amortization tables, the amortization table produced
by the Total Cost Calculator also shows the total cost of
the mortgage at every payment period. Therefore, to solve this
problem, you just need to produce an amortization table and check the total cost
after 10 years and after 30 years. Here's how.
First, Choose "Find total mortgage cost" from the Main Goal
dropdown box. And in the Options section, check "Show amortization schedule" and
check "Include mortgage insurance". This tells the calculator to produce an
amortization table that accounts for private mortgage insurance as part of the
total cost.
Given these settings, the calculator will prompt you for the data it needs.
Provide the data, as shown below.
Describe the Analysis
Main goal:
Describe the Loan
Mortgage type:
Describe the Rate Adjustment Rules
Number of rate adjustments:
Months between rate adjustments:
Ending interest rate (%):
Describe the Costs Paid at Closing
Other costs and fees ($):
Enter Tax and Insurance Info
Annual mortgage insurance ($):
Appraised value of home ($):
After you press the Calculate button, the mortgage calculator
generates a summary report that includes an amortization table. The
amortization table shows that Irving's total mortgage cost over the 30-year
life of the loan will be $468,555.79. The amortization table also shows the
total cost after 10 years. If Irving sells his home (and pays off
the mortgage) after 10 years, his total cost will be $346,920.79.
Problem
Nick is getting a
fixed-rate mortgage. The interest rate is 9%, the loan term is
30 years, and the loan amount is $250,000.
Suppose Nick made an "extra" payment of $100 each month. How long
would it take to pay off the mortgage? How much would Nick save?
Solution:
Use the Prepayment Mortgage Calculator to solve this problem. First, describe the
problem. Choose "Find savings from prepayment" from the Main Goal dropdown box.
The calculator will prompt you for the data it needs. Provide the data,
as shown below.
Describe the Analysis
Main goal:
Describe the Loan
Mortgage type:
Describe the Prepayment Strategy
Amount per prepayment ($):
Then, click the Calculate button. The summary report shows a Prepayment Analysis,
which is reproduced below. Prepayment shortens the loan term from 30 years to
24.42 years; and it reduces the mortgage cost by $105,551.58.
| Number of prepayments per year |
0 |
12 |
Amount per prepayment
|
$0 |
$100 |
| Loan duration |
30 years |
24.42 years |
| Interest expense |
$474,140.88 |
$368,589.30 |
| Savings |
. . . |
$105,551.58 |
Note: This analysis slightly underestimates the benefits of prepayment, because
it doesn't account for possible benefits from reduced property mortgage
insurance (PMI). To account for the benefits of reduced PMI, check the
"Include mortgage insurance" checkbox and repeat the analysis.
Problem
Clark has $15,000, but he needs $500,000 to buy his dream home.
He is considering two options.
- He can get a 30-year, fixed-rate loan for $500,000. The interest rate
would be 7.5%, and he would use his $15,000 to pay 3
discount points.
- He can use his $15,000 as a down payment on the home, and get a
15-year, fixed-rate loan for $485,000 to cover the rest. The interest
rate would be 8%, but there would be no discount points.
If Clark stays in his home for the full 30 years of the mortgage, which loan
should he choose? If Clark sells his home after 5 years, which loan should
he choose? (To keep things simple, assume that there are no closing costs.)
Solution:
Use the Mortgage Comparison Calculator to solve this problem. First,
describe the analysis.
- Choose "Compare two mortgages" from the Main Goal dropdown box.
- Under Loan 1, choose "Fixed-Rate Mortgage" as the mortgage type.
- Under Loan 2, choose "Fixed-Rate Mortgage" as the mortgage type.
- Be sure the "Show amortization schedule" checkbox is checked.
The calculator will prompt you for the data it needs. Provide the data,
as shown below.
Describe the Analysis
Main goal:
Describe the Loan
Mortgage type:
Describe the Costs Paid at Closing
After you press the Calculate button, the Compare Two Mortgages
Calculator generates a summary report that includes an
amortization table. The amortization table shows the total mortgage
cost for each loan, during the life of the loan. The table below shows results
after 5 years (month 60) and after 30 years (month 360). If Clark sells his
home after 5 years, Loan 2 is the best choice. However, if Clark keeps his home
for the life of the mortgage (30 years), Loan 1 is the best choice.
| 60 |
$697,851 |
$689,614 |
| 360 |
$1,273,579 |
$1,296,140 |
Problem
Fred has an adjustable-rate mortgage. There are 15 years left on the
mortgage, and unpaid principal is $150,000. The mortgage has a
periodic rate cap of 1 percent and a
Lifetime rate cap of 12 percent. The current interest rate is 6
percent. The next rate adjustment will
occur in 12 months, and subsequent rate adjustments can occur each 12
months.
Fred can refinance the mortgage with a 15-year, fixed-rate mortgage.
The interest rate for the fixed-rate mortgage would be 8 percent.
To get the new mortgage, Fred will need to pay $3000 in closing costs.
The new mortgage does not require a down payment or points.
Would Fred be better off to keep the existing mortgage, or should he refinance?
Solution:
Use the Refinance Mortgage Calculator to solve this problem. First, describe the
problem.
- Choose "Evaluate refinancing plan" from the Main Goal dropdown box.
- Make sure that the "Show amortization schedule" checkbox is checked.
- Under "Current Loan", in the "Mortgage type" dropdown list box, choose "Adjustable-Rate Mortgage".
- Under "New Loan", in the "Mortgage type" dropdown list box, choose "Fixed-Rate Mortgage".
The calculator will prompt you for the data it needs. Provide the data,
as shown below.
Describe the Analysis
Main goal:
Describe the Loan
Mortgage type:
Describe the Rate Adjustment Rules
Months before first rate adjustment:
Maximum lifetime interest rate (%):
Months between rate adjustments:
Describe the Costs Paid at Closing
Other costs and fees ($):
Then, click the Calculate button. The amortization report shows details for each
month of the loan.
If you input the data and read the amortization report, here is what you will
find. The "breakeven" point for refinancing occurs in the 74th month.
Before the 74th month,
Fred would be better off NOT refinancing. However, after the 74th month, Fred would
save money by refinancing. If he kept the home for the full mortgage term (15 years),
Fred would save $26,024 by refinancing.
In short, if Fred is going to stay in
the house for at least 74 more months, he should refinance. And the longer
Fred lives in his house, the more he will save by refinancing.
Note: This analysis assumes that the adjustable-rate mortgage
"adjusts" to its maximum interest rate of 12 percent - a worst-case scenario.
This might overstate the true cost of the adjustable-rate mortgage.
An alternative analysis would be to employ a best-guess scenario; i.e., guess
the average interest rate over the life of the adjustable-rate mortgage and assume
that the maximum interest rate equals the hypothesized average interest
rate. For more info on this topic, see
Adjustable-Rate Mortgages: Dealing With Uncertainty.
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