If money is invested for 3 years, with interest compounded annually, the future value of the investment varies directly as the cube of (1 + r), where r is the annual interest rate. If the future value of the investment is $4499.46 when the interest rate is 4%, what rate gives a future value of $4244.83

A) 4%

B) 0.02%

C) 20%

D) 2%

Answer: D) 2%

Step-by-step explanation:

Firstly, we would determine the initial amount invested by applying the formula for determining compound interest which is expressed as

A = P (1+r/n) ^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

P = ?

r = 4% = 4/100 = 0.04

A = $4499.46

n = 1 because it was compounded once in a year.

t = 3 years

Therefore,

4499.46 = P (1 + 0.04/1) ^1 * 3

4499.46 = P (1.04) ^3

4499.46 = 1.125P

P = 4499.46/1.125

P = $3999.52

Therefore, when A = $4244.83, then

4244.83 = 3999.52 (1 + r) ^3

4244.83/3999.52 = (1 + r) ^3

1.061 = (1 + r) ^3

Taking cube root of both sides, it becomes

1.02 = 1 + r

r = 1.02 - 1 = 0.02

r = 0.02 * 100 = 2%