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: 43

Answer

(a) After 384 years, the value of the investment would be $\$5,027,378,918$ (b) After 384 years, the value of the investment would be $\$5,224,999,925$

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 (a) We can find the total value of the investment after 384 years when invested at a rate of 5% compounded monthly. $A = P~(1+\frac{r}{n})^{nt}$ $A = (\$24)~(1+\frac{0.05}{12})^{(12)(384)}$ $A = \$5,027,378,918$ After 384 years, the value of the investment would be $\$5,027,378,918$ (b) We can find the total value of the investment after 384 years when invested at a rate of 5% compounded 360 times per year. $A = P~(1+\frac{r}{n})^{nt}$ $A = (\$24)~(1+\frac{0.05}{360})^{(360)(384)}$ $A = \$5,224,999,925$ After 384 years, the value of the investment would be $\$5,224,999,925$
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.