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: 45

Answer

After one year, the second investment at a rate of 5.9% compounded daily would be worth $\$2$ more than the first investment at a rate of 6%.

Work Step by Step

This is the formula we use when we make calculations with simple interest: $A = P~(1+rt)$ $A$ is the final amount in the account $P$ is the principal (the amount of money invested) $r$ is the interest rate $t$ is the number of years We can find the total amount in the account $A_1$ after 1 year when we invest at a rate of 6%. $A = P~(1+rt)$ $A_1 = (\$2000)~[1+(0.06)(1)]$ $A_1 = \$2120$ After 1 year, there will be $\$2120$ in the account. The interest earned is \$120. 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 We can find the total amount in the account $A_2$ after 1 year when investing at a rate of 5.9% compounded daily. $A = P~(1+\frac{r}{n})^{nt}$ $A_2 = (\$2000)~(1+\frac{0.059}{360})^{(360)(1)}$ $A_2 = \$2122$ After 1 year, there will be $\$2122$ in the account. The interest earned is \$122. We can find the difference between the interest earned by the second investment and the first investment. $\$122-\$120 = \$2$ After one year, the second investment at a rate of 5.9% compounded daily earned $\$2$ more interest than the first investment at a rate of 6%.
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