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26 July, 11:54

If you deposit money today in an account that pays 5.5% annual interest, how long will it take to double your money? Round your answer to two decimal places.

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  1. 26 July, 12:06
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    Answer: it take 13.09 years to double your money.

    Step-by-step explanation:

    Assuming the interest was compounded annually, we would apply the formula for determining compound interest which is expressed as

    A = P (1+r/n) ^nt

    Where

    A = total amount in the account at the end of t years

    r represents the interest rate.

    n represents the periodic interval at which it was compounded.

    P represents the principal or initial amount deposited

    From the information given,

    P = P

    A = 2P

    r = 5.5% = 5.5/100 = 0.055

    n = 1 because it was compounded once in a year.

    Therefore,.

    2P = P (1 + 0.055/1) ^1 * t

    2P = P (1.055) ^t

    2P/P = 1.055^t

    2 = 1.055^t

    Taking log of both side, it becomes

    Log2 = tlog1.055.

    0.301 = 0.023t

    t = 0.301/0.023

    t = 13.09 years
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