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27 April, 20:12

Matt invests $1,669 in a saving account with a fixed annual interest rate of 2% compounded 12 times per year. How long will it take for the account balance to reach 1,844.38?

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  1. 27 April, 20:37
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    It will take 4.84 years

    Step-by-step explanation:

    The initial amount that Matt invested was $1669. It means that principal is

    P = 1669

    It was compounded 12 times per year. So

    n = 12

    The rate at which the principal was compounded is 2%. So

    r = 2/100 = 0.02

    The formula for compound interest is

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

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

    A = 1,844.38

    Therefore

    1,844.38 = 1669 (1+0.02/12) ^ (12*t)

    1,844.38/1669 = (1.0017) ^ (12t)

    1.1051 = (1.0017) ^ (12t)

    Taking log to base 10 of both sides, it becomes

    Log 1.1051 = log 1.0017^ (12t)

    Log 1.1051 = 12tlog 1.0017

    0.043 = 0.00074 * 12t

    0.043 = 0.00888t

    t = 0.043/0.00888

    t = 4.84 years
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