Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 8 - Personal Finance - 8.4 Compound Interest - Exercise Set 8.4 - Page 523: 69


$r_e = (1+\frac{r}{n})^{n}-1$, where $r_e$ is the effective annual yield.

Work Step by Step

This is the formula we use when we make calculations with compound interest: $A = P~(1+\frac{r}{n})^{nt}$ $A$ is the final amount in the account $P$ is the principal (the amount of money invested) $r$ is the interest rate $n$ is the number of times per year the interest is compounded $t$ is the number of years This is the formula we use when we make calculations with simple interest: $A = P~(1+r_et)$, where we can let $r_e$ be the effective annual yield. To derive the equation for effective annual yield $r_e$, we can equate the two equations. $P~(1+r_et) = P~(1+\frac{r}{n})^{nt}$ Note that the time period is one year, so $t = 1$. $P~(1+r_et) = P~(1+\frac{r}{n})^{nt}$ $P~(1+r_e) = P~(1+\frac{r}{n})^{n}$ $(1+r_e) = (1+\frac{r}{n})^{n}$ $r_e = (1+\frac{r}{n})^{n}-1$ This is the equation for the effective annual yield.
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