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8 April, 05:05

Payday loans are very short-term loans that charge very high interest rates. You can borrow $200 today and repay $250 in two weeks. What is the compound annual rate implied by this 25 percent rate charged for only two weeks?

32,987.22 percent

30.00 percent

128.25 percent

26.60 percent

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  1. 8 April, 05:12
    0
    32,987.22 percent

    Explanation:

    The rate charged for 2 weeks is 25%, which means that after every 2 weeks the interest rate is compounded. Now in order to find the annual compounded rate we will use the formula (1+Weekly return) ^Number of compounding periods) - 1)

    In this case there are around 52 weeks in a year and because interest is compounded every 2 weeks, there will be 26 compounding periods in a year.

    So we put these numbers in our formula

    ((1+0.25) ^26-1) = 330.8722-1=329.8722

    Now in order to find the percentage we will multiply 329.8722 by 100

    =32,987.22%

    This is our compounded annual rate.
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