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24 July, 21:13

Olivia invested $2,400 in an account paying an interest rate of 4.6/% compounded continuously. Assuming no deposits or withdrawals are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach $3,550?

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  1. 24 July, 22:27
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    8.5

    Step-by-step explanation:

    For continuous compounding, the account value formula is ...

    A = Pe^ (rt)

    where P is the invested amount, r is the annual interest rate, and t is the number of years. We want to find t when ...

    3550 = 2400e^ (.046t)

    ln (355/240) = 0.046t

    t = ln (355/240) / 0.046 ≈ 8.5

    It will take 8.5 years for the value to reach $3550.
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