Question 555690: If Joelle invests $8000 into a retirement account with a 9% interest rate compounded monthly, how long will it take until this single payment has grown in her account to $16,000?
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Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! If Joelle invests $8000 into a retirement account with a 9% interest rate compounded monthly, how long will it take until this single payment has grown in her account to $16,000?
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Compound Interest Formula: A=P(1+i)^n, P=initial investment, i=interest rate per period, n=number of periods, A=amount after n periods.
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For given problem:
P=Initial investment=$8000
i=interest rate per month=.09/12=.0075
A=amount after n months=$16000
..
16000=8000*(1+.0075)^n
16000=8000(1.0075)^n
16000/8000=(1.0075)^n
2=(1.0075)^n
take log of both sides
log(2)=n*log(1.0075)
n=log(2)/log(1.0075)
n≈93.77
ans: It will take about 94 months for Joelle's account to grow to $16,000.
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