Answer to Question #217637 in Financial Math for manpreet

Question

Since the birth of his daughter, 17 years ago, Derek has deposited $150.00 at the beginning of every month into an RESP. The interest rate on the plan was 3.60% compounded monthly for the first 9 years and 4.40% compounded monthly for the next 8 years.

Answer 1

a. Accumulated value of the RESP at the end of 9 years

Future value$=$ C $\times$ $\frac{[(1+r)^n-1]}{r}$ $\times($ 1$+$r$)$

C $=$ periodic deposit $=$ 150

r $=$ periodic interest rate $=$ 3.60%$/$ 12

n$=$ no. of periods $=$ 9yrs $\times$ 12

FV $=$ 150 $\times[$ $($ 1 $+$ 0.03$)^{108} -$ 1$]\times($1$+$ 0.03$)$

FV $=$ 150$\times($$\frac{(0.381976844-1)}{0.00})$ $\times(1.003)$

Future value is;

19, 156.14

b. What would be the accumulated value of the RESP at the end of 17 years

FV $=$ 150 $\times[($$\frac{[(1+0.003)^{108}-1]}{0.003}$ $\times(1+0.003)+$ 150$\times\frac{[1+0.00366]^{96}-1]}{0.00366}$ $\times(1+0.003666)$

17 285.61$+$ 19 156.14

Answer is;

36 441.65