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 7.5 % compounded annually.a. How much will you have saved at the end of five years? (Do not round until the final answer. Then round to the nearest dollar as needed.)b. Find the interest.
Accepted Solution
A:
Answer:Step-by-step explanation: Answer:a. The amount that is saved at the expiration of the 5 year period is $22,769.20¢b. The amount of interest is $2,769.20¢Step-by-step explanation: 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¢