Matthew earns $10 000 per month for the next 25 years,after which he retires.During the first five years of retirement,he withdraws $6000 at the start of each month,after which he dies.His son,Sean,inherits the remainder of Matthew's savings.It is further stipulated in Matthew's will that Sean will be paid the money in equal payments at the start of every month,for the next 20 years.Given a fixed interest rate of 9% p.a. ,calculate the amount of the monthly payments that Sean receives.
A)$98 250
B)$97 340
C)$98 270
D)$97 519

Question

Quizplus · Accepted Answer

To solve this, we use the formula for the future value of an annuity to calculate the amount Matthew saves, then the present value of an annuity to determine the withdrawals during retirement, and finally, the formula for the future value of an annuity to calculate Sean's monthly payments. Given the interest rate of 9% per annum, compounded monthly, the effective monthly interest rate is 0.09/12. The calculations involve determining the future value of Matthew's savings, adjusting for his withdrawals during retirement, and then calculating the equal monthly payments Sean would receive based on the remaining amount.

Matthew Earns $10 000 Per Month for the Next 25