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24 July, 19:15

Sarah invested $1000 in an account paying 5.5% interest compounded semi-annually. How long will it take for the account balance to reach $10,450?

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  1. 24 July, 22:33
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    Answer: it will take 43.25 years

    Step-by-step explanation:

    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 = $1000

    A = $10450

    r = 5.5% = 5.5/100 = 0.055

    n = 2 because it was compounded 2 times in a year.

    Therefore,.

    10450 = 1000 (1 + 0.055/2) ^2 * t

    10450/1000 = (1 + 0.0275) ^2t

    10.45 = (1.0275) ^2t

    Taking log of both sides, it becomes

    Log 10.45 = 2t log 1.0275

    1.019 = 2t * 0.01178 = 0.02356t

    t = 1.019/0.02356

    t = 43.25 years
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