to plan for retirement, boris deposits $1077 each year in an annuity that pays 7.5% interest, compounded…

to plan for retirement, boris deposits $1077 each year in an annuity that pays 7.5% interest, compounded annually. payments will be made at the end of each year. find the total value of the annuity in 28 years. do not round any intermediate computations, and round your final answer to the nearest cent. if necessary, refer to the list of financial formulas.

to plan for retirement, boris deposits $1077 each year in an annuity that pays 7.5% interest, compounded annually. payments will be made at the end of each year. find the total value of the annuity in 28 years. do not round any intermediate computations, and round your final answer to the nearest cent. if necessary, refer to the list of financial formulas.

Answer

Explanation:

Step1: Identify the formula for the future value of an ordinary annuity

The formula for the future value of an ordinary annuity is ( FV = A\times\frac{(1 + r)^{n}-1}{r}), where (A) is the annual payment, (r) is the interest rate per period, and (n) is the number of periods. Here, (A=$1077), (r = 0.075) (since (7.5%=0.075)), and (n = 28).

Step2: Calculate ((1 + r)^{n})

((1 + 0.075)^{28}=(1.075)^{28}) Using a calculator, ((1.075)^{28}\approx7.30377)

Step3: Calculate ((1 + r)^{n}-1)

((1.075)^{28}-1\approx7.30377 - 1=6.30377)

Step4: Calculate (\frac{(1 + r)^{n}-1}{r})

(\frac{6.30377}{0.075}\approx84.05027)

Step5: Calculate (FV)

(FV=1077\times84.05027\approx90522.14)

Answer:

(90522.14)