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22 July, 22:34

A person invests 5000 dollars in a bank. The bank pays 4% interest compounded

annually. To the nearest tenth of a year, how long must the person leave the money

in the bank until it reaches 8200 dollars?

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

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Answers (1)
  1. 22 July, 22:47
    0
    Answer: 12.6 years

    Step-by-step explanation:

    Hi, to answer this question we have to apply the compounded interest formula:

    A = P (1 + r/n) nt

    Where:

    A = Future value of investment (principal + interest)

    P = Principal Amount

    r = Nominal Interest Rate (decimal form, 4/100 = 0.04)

    n = number of compounding periods in each year (1)

    t = years

    Replacing with the values given

    8200 = 5000 (1 + 0.04/1) ^1 (t)

    Solving for t

    8200 = 5000 (1.04) ^t

    8200/5000 = (1.04) ^t

    1.64 = (1.04) ^t

    log 1.64 = log (1.04) ^t

    log 1.64 = t log (1.04)

    log 1.64 / log (1.04) = t

    t = 12.6 years
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