Question

Peter wants to save $500,000 to buy a sport car. He plans to make a deposit of $8,000 each month to achieve this goal. ABC Bank offers a deposit rate of 0.5% per month while DEF Bank offers a deposit rate of 6% with quarterly compounding.

a) Which bank should Peter choose? Briefly explain your answer with appropriate calculations [within 20 words].

b) After making the deposit into the chosen bank as mentioned in part (a), how long does Peter have to wait to achieve his goal if he starts making his first deposit i) today? ii) one month later? iii) six months later?

c) ABC bank has poor credit ratings and the management of the bank has recently offered higher saving interest rates to attract and retain new customers. Peter told you that he can

Answer 1

A)

effective interest rate in case of 0.5% monthly = (1 + 0.005)^12 = 1.0616 = 6.16% annual

in case of 6% compounded quarterly = (1 + 6%/4)^4 = 1.0613 = 6.13% annual

Therefore option with 0.5% monthly is better.

B) since he have to have a future value of 500,000 with monthly payment of 8000 interest rate of 0.5% compunded monthly. Time period is unknown.

8000 * {[(1 + 0.005)^n - 1]/0.005} = 500000

{[(1 + 0.005)^n - 1]/0.005} = 62.5

[(1 + 0.005)^n - 1] = 0.3125

(1.005)^n = 1.3125

where n comes to be 54.5 = apx 55 months

if he makes his first deposit today he will have to wait for 54.5 months

if he makes his first deposit after 1 month he will have to wait for 55.5 months

if he makes his first deposit after 6 month he will have to wait for 60.5 months

C) part C of the question is incomplete