Reducing the Interest Costs of a Mortgage
The total interest paid over the lifetime of a mortgage is a considerable sum of money, often in the hundreds of
thousands of dollars. There are a number of strategies a homeowner can use to reduce the interest costs of a
mortgage
Work with a partner or in a small group.
 Use the TVM Solver to determine the monthly payment.
 Use the ΣInt command to determine the total interest paid.
Answer the following questions.
1. Changing the amortization period
Most homeowners choose an amortization period of 25 years, but amortization periods of 15, 20, and 30
years are also allowed. (Use a mortgage of $200 000 at 5% per year compounded semi-annually.)
a) Complete the following table.
Amortization
Number of
Period
Payments (N)
25
300
15
180
20
240
30
360
Monthly
Payment (PMT)
1163.21
1576.25
1314.25
1067.38
Total Interest
Paid
148962.87
83724.27
115420.05
184257.99
Interest Saved
35295.12
100533.72
68837.94
--
b) How does the monthly payment change as the amortization period increases? Explain.
As the amortization period increases the payment increases as well. (1076.38 to 1576.25)
c) How does the total interest paid change as the amortization period increases? Explain.
As the amortization period increase the interest paid increases by just over $100 000.
d) Why might a homeowner choose a shorter amortization period? Why might a homeowner choose a
longer amortization period?
Shorter – if they can afford higher payments, they will save the 100 000
Longer – if they can’t afford the $500 higher payment, they will have to pay more interest
e) Compare the difference in the monthly payments with the difference in the interest saved for different
pairs of amortization periods. Does the interest saved justify paying more each month? Explain.
For the extra $500 per month the savings of $100 000 would be worth it if you had the extra
money to make the payments.
2. Changing the interest rate
Mortgage interest rates are largely determined by economic conditions. They change frequently over time.
(Use a mortgage of $200 000 amortized over 25 years. Interest is compounded semi-annually.)
a) Complete the following table.
Interest Rate
Year
5%
6%
10%
14%
21.5%
1951
2007
1969
1990
1982
Monthly Payment
(PMT)
1163.21
1279.61
1788.97
2347.75
3453.58
Total Interest Paid
Interest Saved
148962.87
183885.31
336696.57
504332.84
836049.92
-+34922.44
+187733.70
+355369.97
+687087.05
b) How do the monthly payment and the total interest paid change as the interest rate increases? Explain.
The monthly payments and interest increase drastically when the interest rate changes
(especially at more than 10% interest).
c) Does an increase of 4% in the interest rate result in a 4% increase in the total interest paid? Explain.
183885.31(1.04) = 191240.72 – so no, it increases by a lot more than 4%
3. Changing the payment frequency
Many mortgages are repaid with monthly payments, but more frequent payments are also allowed.
 semi-monthly (twice a month; 24 payments a year)
 bi-weekly (every 2 weeks; 26 payments a year)
 weekly (every week; 52 payments a year)
a) Complete the following table. (Use a mortgage of $200 000 at 5% per year compounded semi-annually,
amortized over 25 years.)
Payment
Payments per
Number of
Payment
Interest
Total Interest
Frequency
Year (P/Y)
Payments (N)
(PMT)
Saved
Monthly
12
300
1163.21
148962.87
-306.83
Semi-monthly
24
600
581.01
148602.04
-24.82
Bi-weekly
26
650
536.27
148577.22
-168.83
Weekly
52
1300
268.01
148408.39
-b) Is the interest saved significant when payments are made more often? Explain.
No, there is not much difference in interest paid with changing the payment frequency (with
regular payments).
c) Why might a homeowner choose to make semi-monthly, bi-weekly, or weekly payments instead of
monthly payments?
People will choose their payments based on their pay schedule.
4. Making accelerated payments
Most financial institutions allow “accelerated” weekly and bi-weekly payments. With this option, the weekly
payment is one-quarter of the monthly payment, while the bi-weekly payment is one-half of the monthly
payment.
a) Complete the row for monthly payments and the second and third columns of the accelerated bi-weekly
and accelerated weekly payments. (Use the same mortgage as #3)
Payment
Payments per
Number of
Payment
Interest
Total Interest
Frequency
Year (P/Y)
Payments (N)
(PMT)
Saved
Monthly
12
300
1163.21
148962.87
-Accelerated Biweekly
Accelerated
Weekly
26
558
581.61
124785.96
-24176.91
52
1116
290.80
124516.53
-24446.34
b) Compare the accelerated weekly and accelerated bi-weekly payments with the regular weekly and biweekly payments in question 3a. Why will the mortgage be paid off more quickly with accelerated
payments? The accelerated payments are slightly higher than regular payments.
c) Use the TVM Solver to determine the number of payments it takes to pay off the mortgage with
accelerated bi-weekly payments.
• Open the TVM Solver.
• Enter the known values for I%, PV, PMT, FV, P/Y, and C/Y.
• Move the cursor to N, and press ALPHA ENTER.
d) Use the ΣInt command to determine the total interest paid with accelerated bi-weekly payments. Use
the value of N you determined in part c.
e) Repeat parts c and d for the accelerated weekly payments.
5. Comparing regular and accelerated payments
Compare the tables in questions 3 and 4.
a) Why are the interest savings much greater with accelerated payments than with regular payments?
Because the payments are slightly higher, you end up having a smaller amortization by about
3.5 years, so you save the 3.5 years worth of interest.
b) How many payments are saved by making accelerated payments? How much time does this represent
in years and months?
Accelerated bi-weekly – saved 92 payments (3.5 years)
Accelerated weekly – saved 184 payments (3.5 years)
c) In Canada, the most popular payment frequency is the accelerated bi-weekly option. Why do you think
this is the most popular option?
Most people get paid bi-weekly so they choose a corresponding payment.
WHAT SEEMS TO BE THE BEST WAY TO PAY YOUR MORTGAGE OFF SOONER? WHAT WOULD YOU
RECOMMEND TO ANYONE LOOKING TO GET A MORTGAGE TODAY?
Always pick accelerated payments and pick a smaller amortization if you can afford the payment.