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: 69

Answer

$r_e = (1+\frac{r}{n})^{n}-1$, 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.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.