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# Calculating annual payments for a mortgage amount

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Chinn Wong wishes to purchase a \$600,000 house. She has accumulated a \$120,000 down payment, but she wishes to borrow \$480,000 on a 30-year mortgage. For simplicity, assume annual mortgage payments occur at the end of each year and there are no loan fees.

1. What are Wong's annual payments if her interest rate is:
a. 8%
b. 10%
c. 12%
all compounded annually?

2. Repeat number 1 for a 15-year mortgage.

3. Suppose Wong had to choose between a 30-year and a 15-year mortgage, either one at a low 10% interest rate. Compute the total payments and total interest paid on
a. a 30-year mortgage and
b. a 15-year mortgage.

#### Solution Preview

Chinn Wong wishes to purchase a \$600,000 house. She has accumulated a \$120,000 down payment, but she wishes to borrow \$480,000 on a 30-year mortgage. For simplicity, assume annual mortgage payments occur at the end of each year and there are no loan fees.

1. What are Wong's annual payments if her interest rate is:
a. 8%

This is a case of ordinary annuity.
Periodic Payment=C=?
Number of payments=n=30
Rate of return=r=8% (annual)
Mortgage amount =Present value of 30 annual payments =PV=\$480,000
PV= C/r*(1-1/(1+r)^n)
480000=C/8%*(1-1/(1+8%)^30)
480000=C*11.2578
C=480000/11.2578=\$42637.10
Annual payments=\$42637.10

b. 10%
This is a case of ordinary annuity.
Periodic Payment=C=?
Number of payments=n=30
Rate of return=r=10% (annual)
Mortgage amount =Present value of 30 annual payments ...

#### Solution Summary

Its a three part problem. Solution describes the steps to calculate annual payments for a mortgage at different discount rates for two different tenures. It also calculate total payments and total interest paid in different cases.

\$2.19