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29 June, 00:12

Joanie takes a $6000 loan to pay for her car. The annual interest rate on the loan is $12%. She makes no payments for 4 years, but has to pay back all the money she owes at the end of 4 years. How much more money will she owe if the interest compounds quarterly than if the interest compounds annually?

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  1. 29 June, 00:36
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    The amount due under quarterly compounding is higher by = $ 187.12

    Explanation:

    To determine the amount money by which the quarterly compunding is greater, we would compare the total sum due under the two compounding options.

    This is done below:

    Quarterly compounding

    FV = A * (1+r) ^n

    PV - principal amount owed = 6,000

    r - quarterly interest rate = 12%/4 = 3% per three month

    n - number of quarters in 4 years = 4 * 4 = 16

    Loan amount due with interest after 4 years

    = 6,000 * (1.03) ^ (48) = 9628.23

    Annual compounding

    PV - principal amount owed = 6,000

    r - annual interest rate = 12% =

    n - number of years = 4

    Loan amount due = 6,000 * (1.12) ^ (4) = 9,441.12

    The amount due under quarterly compounding is higher by

    = 9628.23 - 9,441.12

    =$ 187.12
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