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2 July, 22:05

Piscataway National Bank pays compound interest on savings accounts, but at different rates depending on the amount of the account balance. It pays an annual effective rate of 3% on balances under $10,000, but 4% on balances greater than or equal to $10,000. Suppose that you make a $5,000 deposit. How many years does it take for the account balance to reach $15,000?

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  1. 2 July, 23:25
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    It will take 4.2 years

    Explanation:

    The amount due in the future when a sum of money is invested at a particular interest rate for certain number of years is called Future or compound value.

    To calculate the compound value, we use the formula below:

    FV = PV * (1+r) ^n

    FV - future value, PV - Present value, r - interest rate, n - number of years

    In this question,

    FV - 15,000, PV - 5000, r - 3%, n-?

    Substituting this value we have:

    15,000 = 5000 * (1+0.03) ^n

    15000 = 5000 * 1.03^n

    1.03^n = 15,000/5000

    1.03^n = 3

    log 1.03^n = Log 3

    n = Log 3/log 1.03

    n = 4.18735

    It will take about 4.2 years for the account to reach $15,000
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