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Suppose $1,000 is compounded quarterly for 4 years. What rate is needed to reach a total of $2,000? Round to the nearest tenth of a percent.

  • precalculus -

    let the quarterly rate be i

    1000(1 + i)^16 = 2000
    (1+i)^16 = 2
    take the 16th root of both sides

    1+i = 2^(1/16)
    1+i = 1.04427
    i = .04427

    the quarterly rate is 4.427 %
    the annual rate compounded quarterly is 17.7%

    (time to have that mathbook updated.
    a 17% interest rate is a fantasy these days)

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