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4 December, 14:39

Rhonda deposited $4,227.29 into a savings account with an interest rate of 4.9% compounded monthly. About how long will it take for the account to be worth $9,000?

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  1. 4 December, 14:44
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    Since we multiply the amount of money by 1.049 (which is 1+4.9% by moving the decimal 2 spots to the right) every month, we have 4227.29 (the original rate) * (1.049) ^x/1=A (amount) due to that we compound it once per month and x is the amount of months. This is a slightly edited version of A=P (1+r/n) ^ (nt) where n is the number of times compounded per year and t is the time in years - we simply switch years to months here.

    Going back to our equation, we divide both sides by 4227.29 to get

    A/4227.29 = (1.049) ^x. Since the end amount is 9000, we have

    9000/4227.29 = (1.049) ^x. Solving for x, we have

    log (base1.049) (9000/4227.29) = around 15.796522523 months
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