Question

1. Mr A wants to purchase a motor vehicle. The vehicle that he is interested in has a retail price of R350 000. Mr A can only afford a monthly repayment of R6 500. If financed, the vehicle will be financed over a 5 year period at a rate of 11%. Advise Mr A on the residual value amount that he should negotiate on the contract to keep his repayments at R6 500 per month.

2. Mr A entered into the following investment. He is investing a monthly amount of R10 000 for the next 3 years with Bank ABC. After the 3 year period the Bank is repaying Mr A an amount of R450 000. What is the rate of interest Mr A is earning on his investment?

Answer 1

1.

Monthly loan payments = R6500

Monthly interest rate = 11%/12 = 0.9167% = 0.009167

Number of monthly payments = 5 years * 12 = 60

Loan amount paid by monthly payments = Present value of monthly payments

Present value of annuity = Annuity amount*{1-(1+r)^-n}/r

Loan amount repaid by monthly payments = R6500*(1-1.009167^-60)/0.009167 = R298954.72

Remaining amount to be repaid by residual value = R350000 – R298954.72 = R51045.28

Residual value = R51045.28*1.009167⁶⁰ = R88,252.99

2.

Monthly investment = R10000

Number of months in 3 years = 3 *12 = 36

Future value after 3 years = R450,000

Future value of annuity = Annuity amount*{(1+r)ⁿ-1}/r

R450000 = R10000*{(1+r)³⁶-1}/r

Solving above, r = 1.24%

Annual rate = 1.24%*12 = 14.88%