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10 November, 21:52

Yolanda invests $5000 in an account that earns 1.4% annual interest compounded monthly.

How many years will it take for the balance of this account to reach $8000?

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  1. 10 November, 22:03
    0
    33 years, 7 months

    Step-by-step explanation:

    Using the compound interest formula Accrued Amount = P (1 + r/n) ^ (nt)

    where Accrued amount (A) is the expected future balance

    A = $8000

    P = principal; $5000

    r = 1.4% = 0.014

    t = number of years

    n = number of times interest is compounded = 12 for monthly

    Therefore

    8000 = 5000 (1 + 0.014/12) ^ (12t)

    Therefore

    (1.001167) ^12t = 8000/5000

    (1.001167) ^12t = 1.6

    finding the log of both sides

    12t x log 1.001167 = log 1.6

    12t = log 1.6 / log 1.001167

    12t = 402.98

    t = 402.98/12

    t = 33.58

    hence time to increase the balance is 33 years, 7 months
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