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Suppose you invested $3000 at 9% compounded monthly. About how long would it take...

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Suppose you invested $3000 at 9% compounded monthly. About how long would it take before you had $4700

 

 

 

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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`

 

Therefore,

`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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