Questions: Suppose that you earned a bachelor's degree and now you're teaching high school. The school district offers teachers the opportunity to take a year off to earn a master's degree. To achieve this goal, you deposit 4000 at the end of each year in an annuity that pays 6% compounded annually. Formulas In the following formulas, P is the deposit made at the end of each compounding period, r is the annual interest rate of the annuity in decimal form, n is the number of compounding periods per year, and A is the value of the annuity after t years. A = (P[(1+r)^t - 1])/r A = (P[(1 + (r/n))^(nt) - 1])/(r/n) P = (A(r/n))/[(1 + (r/n))^(nt) - 1] In the following formulas, P is the principal amount deposited into an account, r is the annual interest rate in decimal form, n is the number of compounding periods per year, and A is the future value of the account after t years. A = P(1+r)^t A = P(1 + (r/n))^(nt) a. After 5 years, you will have approximately . (Do not round until the final answer. Then round to the nearest dollar as needed.) b. The interest is approximately . (Use the answer from part a to find this answer.)

Transcript text: Suppose that you earned a bachelor's degree and now you're teaching high school. The school district offers teachers the opportunity to take a year off to earn a master's degree. To achieve this goal, you deposit $\$ 4000$ at the end of each year in an annuity that pays $6 \%$ compounded annually. Formulas In the following formulas, P is the deposit made at the end of each compounding period, $r$ is the annual interest rate of the annuity in decimal form, n is the number of compounding periods per year, and A is the value of the annuity after $t$ years. \[ A=\frac{P\left[(1+r)^{t}-1\right]}{r} \quad A=\frac{P\left[\left(1+\frac{r}{n}\right)^{n t}-1\right]}{\left(\frac{r}{n}\right)} \quad P=\frac{A\left(\frac{r}{n}\right)}{\left[\left(1+\frac{r}{n}\right)^{n t}-1\right]} \] In the following formulas, $P$ is the principal amount deposited into an account, $r$ is the annual interest rate in decimal form, n is the number of compounding periods per year, and $A$ is the future value of the account after $t$ years. \[ A=P(1+r)^{t} \quad A=P\left(1+\frac{r}{n}\right)^{n t} \] a. After 5 years, you will have approximately \$ $\square$ . (Do not round until the final answer. Then round to the nearest dollar as needed.) b. The interest is approximately $\$$ $\square$ . (Use the answer from part a to find this answer.)