If money is invested for 3 years, with interest compounded annually, the future value of the investment varies directly as the cube of (1 +

Question

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%

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Kinsley 2 weeks 2021-10-08T03:30:53+00:00 1 Answer 0

Answers ( )

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    2021-10-08T03:32:11+00:00

    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%

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45:7+7-4:2-5:5*4+35:2 =? ( )