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7 April, 08:08

A local bank will pay you $275 at the end of each year for your lifetime if you deposit $4,400 in the bank today. If you plan to live forever, what interest rate is the bank paying? (Enter your answers as a percent rounded to 2 decimal places.)

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  1. 7 April, 08:10
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    Interest rate = 6 ... 3%

    Explanation:

    An investment that pays a fixed amount for life is called a perpetuity. The worth of a perpetuity today is the present value of the future cash flow. Using the present value of the perpetuity formula, we can work out the interest rate as follows:

    PV = A * 1/r

    Where PV = present value, r - Interest rate, A - annual cash flow

    4,400 = 275 * 1/r

    cross multiply

    4,400 * r = 275

    divided both sides by 4,400

    r = 275/4400

    r = 0.0625 * 100

    r = 6.25%

    r = 6.3%

    Interest rate = 6 ... 3%
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