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28 March, 17:14

John Jamison wants to accumulate $62,154 for a down payment on a small business. He will invest $34,000 today in a bank account paying 9% interest compounded annually. Approximately how long will it take John to reach his goal? (Do not round intermediate calculations. Round your final answers to nearest whole dollar amount.)

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  1. 28 March, 20:02
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    It will take him 7 years.

    Explanation:

    Hi! We need to calculate the amount of time that it requires an investment of $34000 to reach $62154 at an interest rate of 9% annually.

    By using the formula of Present Value we can isolate n:

    The formula is:

    PV=Ct/[ (1+r) ^n]

    Ct = cash flow at t time

    r = rate

    n = period of time

    To calculate how many years, we need to isolate n from the PV formula:

    n=[ln (Ct/PV) ]/ln (1+r)

    n=ln (62154 / 34000) / ln (1+0,09)

    n=7
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