Question

Use a formula to calculate the amount of money you would have if you invest $3000 at a rate of 5% compounded quarterly, for 3 years. (Remember y=a(1+r)^n) )

How would this value change if the rate was 1.5% compounded monthly for the same period?

Answer 1

At 5% compounded quarterly, the amount of $3,000 would be $3,482.

At 1.5% compounded monthly, the amount of $3,000 would be $3,138.

Explanation:

Option 1:

Rate = r = 5%

Times = b = 4

y = a (1 + r)ⁿ

For compounded quarterly the rate of interest and Number of years will be written as follows:

y = a [1 + (r / b)]ⁿᵇ

y = $3,000 [1 + (0.05 / 4]³ ˣ ⁴

y = $3,000 [1 + 0.0125]¹²

y = $3,000 [1.0125]¹²

y = $3,000 x 1.160755

y = $3,482

Option 2:

Rate = r = 1.5%

Times = b = 12

y = a (1 + r)ⁿ

For compounded monthly the rate of interest and Number of years will be written as follows:

y = a [1 + (r / b)]ⁿᵇ

y = $3,000 [1 + (0.015 / 12]³ ˣ ¹²

y = $3,000 [1 + 0.00125]³⁶

y = $3,000 [1.00125]³⁶

y = $3,000 x 1.045998

y = $3,138

Hence As compared to Option 1, Option 2 has low rate of return by $344. Therefore Option 1 should be selected.