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11 February, 18:29

Find the balance on the account after 6.2 years if $150000 was invested at an annual interest rate of 2.76% and the interest was compounded continuously. What is the accumulated value if the money is compounded continuously? Round to the nearest cent.

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  1. 11 February, 20:30
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    Annual compounding gives $177,582.70

    Continuous compounding gives $ 177,994.97

    Step-by-step explanation:

    In the first place, the balance on account can be computed using the future value formula given below:

    FV=PV * (1+r) ^N

    FV is the future value which is unknown

    PV is the amount invested at time zero which is $150,000

    r is the rate of return on the investment at 2.76%

    N is the period of investment which is 6.2 years

    FV=$150,000 * (1+2.76%) ^6.2

    FV=$ 177,582.70

    However if the continuous compounding is opted for the accumulated value is computed thus:

    FV=PV * e^ (rs*N)

    where e is constant figure given as 2.7182818

    rs is the rate of return at 2.76%

    N is 6.2 years

    PV is $150,000

    FV=$150,000*2.7182818^ (2.76%*6.2)

    FV=$150,000*1.186633134

    FV=$ 177,994.97
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