## Thinking Mathematically (6th Edition)

Published by Pearson

# Chapter 8 - Personal Finance - 8.5 Annuities, Methods of Saving, and Investments - Exercise Set 8.5: 24

#### Answer

$P = \frac{A~(\frac{r}{n})}{~(1+\frac{r}{n})^{nt}~-1}$ The resulting formula describes the amount of the periodic deposit $P$ required in an annuity.

#### Work Step by Step

$A = \frac{P~[(1+\frac{r}{n})^{nt}~-1]}{(\frac{r}{n})}$ $P = \frac{A~(\frac{r}{n})}{~(1+\frac{r}{n})^{nt}~-1}$ The resulting formula describes the amount of the periodic deposit $P$ required in an annuity if we want to end up with a final amount, $A$, with an interest rate of $r$ compounded $n$ times per year for a time of $t$ years.

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