A person invests 2000 dollars in a bank. The bank pays 6.25% interest compounded semi-annually. To the nearest tenth of a year, how long mus

Question

A person invests 2000 dollars in a bank. The bank pays 6.25% interest compounded semi-annually. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 5900 dollars?

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Tài Đức 4 years 2021-08-03T12:02:22+00:00 1 Answers 11 views 0

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  1. minhkhoi
    0
    2021-08-03T12:03:39+00:00
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    9514 1404 393

    Answer:

      17.6 years

    Step-by-step explanation:

    The compound interest formula is useful for figuring this out.

      A = P(1 +r/n)^(nt) . . . . . interest r compounded n per year for t years

    Filling in the given values and solving for t, we have …

      5900 = 2000(1 +.0625/2)^(2t)

      2.95 = 1.03125^(2t) . . . . divide by 2000, simplify

      log(2.95) = 2t×log(1.03125) . . . . take logarithms

      t = log(2.95)/(2×log(1.03125) . . . . divide by the coefficient of t

      t ≈ 17.6

    The person must leave the money in the bank for 17.6 years.

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