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15 September, 11:23

Isaac invested $460 in an account paying an interest rate of 2.4% compounded daily. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $690?

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  1. 15 September, 12:06
    0
    t = 17 years

    Step-by-step explanation:

    The formula for interest

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

    where a is the amount in the account, p is the principal, r is the rate, n is the number of times compounded per year and t is the time in years

    Substituting in what we know

    690 = 460 (1+.024/365) ^ 365t

    690/460 = (1+.024/365) ^ 365t

    1.5 = (1+.024/365) ^ 365t

    Taking the log of each side

    log (1.5) = 365t log (1+.024/365))

    Dividing each side by (1+.024/365)

    log (1.5) / log (1+.024/365) = 365t

    divide each side by 365

    1/365 log (1.5) / log (1+.024/365) = t

    t = 16.8949

    To the nearest year

    t = 17
  2. 15 September, 13:32
    0
    17 years

    Step-by-step explanation:

    460 (1 + (2.4/365) %) ^t = 690

    1.000065753425^t = 1.5

    t ln1.000065753425 = ln1.5

    t = 6,166.6535619036 days

    6,166.6535619036/365

    = 16.8949412655 years
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