Question

1. Suppose you wish to buy a house for $500,000. You make a 25% down payment and borrow the rest at an interest rate of 6% for 30 years.

(a) What is your annual repayment?

(b) Repeat the above assuming a mortgage term of 25 years.

2. Suppose you borrow $20,000 to buy a car. The interest rate is 11% and the loan is for 8 years.

(a) What is your annual repayment?

(b) What is the remaining balance after 3 years?

(c) What is the remaining balance after 7 years?

Answer 1

1. a. PVA _{6%, n=30} = [ { 1 - ( 1 / 1.06 ) ³⁰ } / 0.06 ] = 13.76483

Net borrowing = $ 500,000 x 0.75 = $ 375,000.

Annual installment = $ 375,000 / 13.76483 = $ 27,243.34

b. PVA _{65, n=25} = [ { 1 - ( 1 / 1.06) } / 0.06 ] = 12.78336

Annual installment = $ 375,000 / 12.78336 = $ 29,335.01

2.

PVA _{11%, n=8} = [ { 1 - ( 1 / 1.11 ) ⁸ } / 0.11 ] = 5.14612

a. Annual Installment = 20,000 / 5.14612 = $ 3,886.42

Loan Amortization Schedule:

Year	Amount	Interest	Principal Repaid	Loan Outstanding
0				20,000
1	3,886.42	2,200	1,686.42	18,313.58
2	3,886.42	2,014.49	1,871.93	16,441.65
3	3,886.42	1,808.58	2,077.84	14,363.81
4	3,886.42	1,580.02	2,306.40	12,057.41
5	3,886.42	1,326.32	2,560.10	9,497.31
6	3,886.42	1,044.70	2,841.72	6,655.59
7	3,886.42	732.11	3,154.31	3,501.28
8	3,886.42	385.14	3,501.28	0

b. Balance remaining after 3 years : $ 14,363.81

c. Balance remaining after 7 years : $ 3,501.28