Question

You are buying a car at a cost of $42,000 by taking a loan. The nominal interest rate is 9% per annum compounded monthly. The bank offers 2 options for the structure of the repayments. Option 1: The loan will be repaid over 10 years by equal month-end-instalments.

a) Calculate the monthly instalment. (1 mark)

b) Calculate the interest component for the 20th repayment.

c) Calculate the loan outstanding immediately after 8 years (immediately after the payment on that date). d) Hence or otherwise, calculate the cumulative principal repayments during the 9th year.

Option 2: Month-end-instalments of $X will be made for the first 3.5 years. Then the bank offers you a payment free period (i.e., no repayments required) of 1 year. After that, the remaining balance will be repaid over 3.5 years by month-end-instalments of $2X.

e) Calculate X.

Answer 1

A

Monthly Installment

P * R/M * (1+ R/M)n / [ (1 + R/M)n - 1]

where P = Loan

R = Rate of Interest

N = No. of period

Monthly Installemt =

$42000 * (9%/12) * (1+ 9%/12)120 / (1+9%/12)120 - 1

$532.04

B

Interest Copound of 20th repayment

$281.90

C

Loan Outstanding Immediately after 8 years

$11,651.21

D

Cumulative princiapal repayment during 9th year

$5,561.07

( all answers are marked with color in table)

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