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?

Question

Mathematics

Rylee Kline

18 September, 10:36

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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Gloria Cervantes · Answer 1

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