Step 1
Given; 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 $1000 at the end of each year in an annuity that pays 5% compounded annually. How much will you have saved at the end of five years? Find the interest.
a. After 5 years, you will have approximately $
(Do not round until the final answer. Then round to the nearest dollar
as needed.)
Step 2
The formula for an annuity is;
[tex]FV=P[\frac{(1+r)^t-1}{r}][/tex]where;
[tex]\begin{gathered} P=1000 \\ r=\frac{5}{100}=0.05 \\ t=5 \end{gathered}[/tex][tex]FV=1000[\frac{(1+0.05)^5-1}{0.05}][/tex][tex]FV=\text{ \$}5525.63125[/tex]Thus the answer is; After 5 years you will have approximately;
[tex]FV=\text{ \$5526}[/tex]
The interest will be;
[tex]\begin{gathered} I=FV-(P(t)) \\ I=5526-(1000(5))=5526-5000=\text{ \$526} \end{gathered}[/tex]