Question 5.S-TP.4: Calculating the Number of Periods You’ve been offered an inv...

Calculating the Number of Periods You’ve been offered an investment that
will pay you 9 percent per year. If you invest $15,000, how long until you have
$30,000? How long until you have $45,000?

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The basic equation is this:
$30,000 = $15,000 × (1  + .09 )^{t}
2 = (1  + .09 )^{t}
If we solve for t , we find that t = 8.04 years. Using the Rule of 72, we get 72/9 = 8 years, so once again our answer looks good. To get $45,000, verify for yourself that you will have to wait 12.75 years.

 

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