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: 22

Answer

(a) After 1 year, there will be \$12,799.22 in the account. (b) The effective annual yield is 6.66%

Work Step by Step

(a) 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 $A = P~(1+\frac{r}{n})^{nt}$ $A = (\$12,000)~(1+\frac{0.065}{4})^{(4)(1)}$ $A = \$12,799.22$ After 1 year, there will be \$12,799.22 in the account. (b) This is the formula we use when we make calculations with simple interest: $A = P~(1+rt)$ $1+rt = \frac{A}{P}$ $r = \frac{\frac{A}{P}-1}{t}$ $r = \frac{\frac{\$12,799.22}{\$12,000}-1}{1}$ $r = 0.0666$ The effective annual yield is 6.66%
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.