Question

Cathy is a supermarket manager who has $50000 to invest for a period of 5 years, and the bank offers a choice of two investment schemes, Plan A and Plan B. Under Plan A she would receive an annual interest rate of 8.30% compounded quarterly, while under Plan B she would receive an annual interest rate of 8.25% compounded monthly.

(a) Calculate the amount of interest Cathy would earn under each plan.

(b) Which plan should Cathy choose? How much extra interest would she earn over the other plan?

Answer 1

Given

Principal=$\$50000$

Number of years, n,= $5years$

$FV=PV (1+\frac{r}{m})^{nm}$

1. Plan A:

r= $8.30\%$

$m=4$

$\therefore FV_5=\$50000(1+\frac{0.083}{4})^{5×4}$

$FV_5=\$75397.64$

Interest earned on plan A$\$75397.64-\$50000=\$25397.64$

Plan B:

$r=8.25\%$

$m=12$

$\therefore FV_5=\$50000(1+\frac{0.0825}{12})^{5×12}$

$FV_5=\$75422.94$

Interest earned on plan B

$\$75422.94-\$50000=\$25422.94$

2. Cathy should choose plan B. The extra interest earned by choosing plan B over plan A is $\$25422.94-\$25397.64=\$25.3$