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2 April, 12:53

Jaquin hopes to earn $700 in interest in 1.6 years time from $56,000 that he has available to invest. To decide if it's feasible to do this by investing in an account that compounds monthly, he needs to determine the annual interest rate such an account would have to offer for him to meet his goal. What would the annual rate of interest have to be? Round to two decimal places.

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  1. 2 April, 14:41
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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 = $56,000

    A = 56000 + 700 = $56700

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

    t = 1.6 years

    Therefore,

    56700 = 56000 (1 + r/12) ^12 * 1.6

    56700/56000 = (1 + r/12) ^19.2

    56700/56000 = (1 + 0.0833r) ^19.2

    1.0125 = (1 + 0.0833r) ^19.2

    Taking log of both sides, it becomes

    Log 1.0125 = 19.2log (1 + 0.0833r)

    0.005395/19.2 = log (1 + 0.0833r)

    0.005395/19.2 = log (1 + 0.0833r)

    0.00028 = log (1 + 0.0833r)

    Taking inverse log of both sides, it becomes

    10^0.00028 = 10^log (1 + 0.0833r)

    1.00064 = 1 + 0.0833r

    0.0833r = 1.00064 - 1

    0.0833r = 0.00064

    r = 0.00064/0.0833

    r = 0.0077

    Multiplying by 100, it becomes

    0.77%
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