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 6.5% compounded annually.
a. how much will you have saved at the end of 5 years?
b. Find the interest.

Since the amount that is deposited every year for a period of five years is $4,000 and the rate of the interest is 6.5%. We can always calculate the amount that is saved at the expiration of the five years.

We will first state the formula for calculating the future value of annuity:-

Future value of annuity =

[tex]P[\frac{(1 + r)^{t}-1 }{r}][/tex]

Where P is the amount deposited per year.

r is the rate of interest

t is the time or period

and in this case, the actual value of P = $4,000

rate of interest, r is 6.5% = 0.065

time, t is 5 years.

Substituting e, we have:

Fv of annuity =

[tex]4,000[\frac{(1 + 0.065)^{5}-1 }{0.065 }][/tex]

= 4,000 × [((1.065)^5)- 1/0.065]

= 4,000 × [(1.37 - 1)/0.065]

= 4,000 × (0.37/0.065)

= 4,000 × 5.6923

= $22,769.20¢

a. Therefore the amount that is saved at the end of the five (5) years is $22,769.20¢

b. To find the interest, we will calculate the amount of deposit made during the period of five years and subtract the sum from the current amount that is saved ($22,769.29¢).

Since I deposited 4,000 every year for five years, the total amount of deposit I made at the period =

4,000 × 5 = $20,000

The amount of interest is then = $22,769.20¢ - $20,000 = $2,769.20¢