Question

suppose that you earned a bachelors degree and now youre teaching high school. the school district offers teachers the opportunity to take a year off to earn a masters degree. to achieve this goal, you deposit $2000 at the end of each year in an annuity that pays 5.5% compounded annually.
a. how much will you have saved at the end of five years?
b. find the interest.
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a. after 5 years, you will have approximately $
(do not round until the final answer. then round to the nearest dollar as needed.)

Explanation:

Step1: Identify future value formula

The future value of an ordinary annuity is given by:
$$FV = P \times \frac{(1 + r)^n - 1}{r}$$
where $P = 2000$, $r = 0.055$, $n = 5$.

Step2: Calculate $(1 + r)^n$

$$(1 + 0.055)^5 = 1.055^5 \approx 1.30696$$

Step3: Compute numerator and denominator

$$(1.30696 - 1) = 0.30696$$
$$\frac{0.30696}{0.055} \approx 5.58109$$

Step4: Find total saved amount

$$FV = 2000 \times 5.58109 \approx 11162.18$$
Round to nearest dollar: $\$11162$

Step5: Calculate total deposits

$$\text{Total Deposits} = 2000 \times 5 = 10000$$

Step6: Compute earned interest

$$\text{Interest} = 11162 - 10000 = 1162$$

Answer:

a. $\$11162$
b. $\$1162$