Katie invests $5,000 in an account earning 4% interest, compounded annually for 5 years. Two years after Katie's initial investment, Emily invests $10,000 in an account earning 4% interest, compounded annually for 3 years. Given that no additional deposits are made, compare the amount of interest earned after the interest period ends for each account. (round to the nearest dollar)

Answer:Emily will earn $166 more interest than Katie after the interest period ends for each account.Step-by-step explanation:Formula for compound interest is:   [tex]A=P(1+\frac{r}{n})^n^t[/tex], where P is the initial amount, A is the final amount with interest,  r  is the rate of interest in decimal,  n is the number of compounding in a year and  t  is the time durationKatie invests $5,000 in an account earning 4% interest, compounded annually for 5 years. That means here,  [tex]P= 5000, r= 4\%=0.04, n=1[/tex] and [tex]t=5[/tex]So,  [tex]A= 5000(1+\frac{0.04}{1})^(^1^)^(^5^) = 5000(1.04)^5 = 6083.26... \approx 6083[/tex]Thus, the amount of interest earned by Katie [tex]= \$6083-\$5000 = \$1083[/tex]Now, Emily invests $10,000 in an account earning 4% interest, compounded annually for 3 years. That means here,  [tex]P= 10000, r= 4\%=0.04, n=1[/tex] and [tex]t=3[/tex]So,  [tex]A= 10000(1+\frac{0.04}{1})^(^1^)^(^3^) = 10000(1.04)^3 = 11248.64 \approx 11249[/tex]Thus, the amount of interest earned by Emily [tex]= \$11249-\$10000 = \$1249[/tex]After the interest period ends for each account, Emily will earn ($1249 - $1083) or $166 more interest than Katie.