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20 May, 03:32

Tamira invests $5,000 in an account that pays 4% annual interest. How much will there be in the account after 3 years if the interest is compounded annually, semi-annually, quarterly, or monthly?

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  1. 20 May, 05:24
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    Step-by-step explanation:

    We would apply 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 = 5000

    r = 4% = 4/100 = 0.04

    t = 3 years

    1) compounded annually

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

    Therefore,

    A = 5000 (1 + 0.04/1) ^1 * 3

    A = 5000 (1.04) ^3

    A = $5624.32

    2) compounded semi annually

    n = 2 because it was compounded twice in a year.

    Therefore,

    A = 5000 (1 + 0.04/2) ^2 * 3

    A = 5000 (1.02) ^6

    A = $5630.81

    3) compounded quarterly

    n = 4 because it was compounded 3 times in a year and n = 12/3 = 4.

    Therefore,

    A = 5000 (1 + 0.04/4) ^4 * 3

    A = 5000 (1.01) ^12

    A = $5634.13

    4) compounded monthly

    n = 12 because it was compounded 12 times in a year.

    Therefore,

    A = 5000 (1 + 0.04/12) ^12 * 3

    A = 5000 (1.0033) ^36

    A = $5629.62
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