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5 September, 10:03

An investment of P dollars increased to A dollars in t years. If interest was compounded continuously, find the interest rate. (Round your answer to the nearest whole number.)

A = 4482, P = 1000, t = 25

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  1. 5 September, 10:13
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    Answer: the interest rate is 6%

    Step-by-step explanation:

    The formula for continuously compounded interest is

    A = P x e (r x t)

    Where

    A represents the future value of the investment after t years.

    P represents the present value or initial amount invested

    r represents the interest rate

    t represents the time in years for which the investment was made.

    e is the mathematical constant approximated as 2.7183.

    From the information given,

    A = $4482

    P = 1000

    t = 25 years

    Therefore,

    4482 = 1000 x 2.7183^ (r x 25)

    4482/1000 = 2.7183^25r

    4.482 = 2.7183^25r

    Taking ln of both sides, it becomes

    Ln 4.482 = 25rLn2.7183

    1.5 = 25r

    r = 1.5/25 = 0.06

    r = 0.06 * 100 = 6%
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