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4 December, 00:38

Suppose you invest $1000 at an interest rate of 6%, compounded annually. Calculate the equivalent interest rate under continuous compounding (find the interest rate r that would give the same result if interest were compounded continuously). Hint: You can consider the situation for 1 year (let t=1).

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  1. 4 December, 00:47
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    The equivalent interest rate under continuous compounding is 5.8%

    Explanation:

    Annual compounding

    A = P (1+r) ^n

    P = $1,000

    r = 6% = 0.06

    n = 1 year

    A = 1000 (1+0.06) ^1 = 1000 (1.06) = $1060

    Continuous compounding

    A = Pe^rt

    A = $1060

    P = $1000

    t = 1 year

    1060 = 1000e^r

    e^r = 1060/1000 = 1.06

    e^r = 1.06

    r = ln 1.06 = 0.058 = 5.8%
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