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17 September, 06:55

You are considering two ways of financing a spring break vacation. You could put it on your credit card, at 14 %14% APR, compounded monthly, or borrow the money from your parents, who want an interest payment of 8 %8% every six months. Which is the lower rate? (Note: Be careful not to round any intermediate steps less than six decimal places.)

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  1. 17 September, 09:55
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    Credit card is at lower rate at 14.93% interest rate

    Explanation:

    Data provided in the question:

    APR on credit card = 14% compounded monthly

    Interest rate from parents = 8% compounded every six months

    Now,

    Annual interest rate = (1 + r) ⁿ - 1

    Here,

    r is the interest rate for the period

    n is the total period

    Thus,

    For the credit card

    since compounded monthly

    Interest rate per month, r = 14% : 12 = 1.167% = 0.01167

    Number of periods, n = 12

    Therefore,

    Annual interest = (1 + 0.01167) ¹² - 1 = 0.1493

    or

    = 0.1493 * 100% = 14.93%

    For borrowing from parents

    since compounded every six months

    Number of periods, n = 12 months : 6 = 2

    Interest rate, r = 8% = 0.08

    Therefore,

    Annual interest = (1 + 0.08) ² - 1 = 0.1664

    or

    = 0.1664 * 100% = 16.64%

    Credit card is at lower rate at 14.93% interest rate
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