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%.
