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The investment is compounded monthly. Therefore monthly interest rate is,
`i = 9/12 %`
`i = 0.75%`
`i = 0.0075`
We know the future value of an investment after n time periods is given by,
`FV = (PV)(1+i)^n`
`4700 = 3000xx(1+0.0075)^n`
`(1.0075)^n = 4700/3000`
Taking log of both sides.
`n log 1.0075 = log 4700 - log 3000`
`n = (3.672098 - 3.477121)/0.003245`
`n = 60.08`
Therefore, iit would take approximately 60 months for the investment to be $4700, but idealy it would take 61 months to have $4700 or more.
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