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%

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%

multiply by 2 the previous number and multiply by -1 for the next answer,

(note I haven't done these in a while so I think it's supposed to be like this, sorry if I'm wrong)