A retirement plan guarantees to pay to you or your estate a fixed amount for 20 years.At the time of retirement you will have $250,000 to your credit in the plan.The plan anticipates earning 9% interest compounded monthly.How much will your monthly benefits be,paid at the end of each month?

Question

Quizplus · Accepted Answer

To calculate the monthly benefits, we need to use the present value formula for an annuity:

PV = Payment * [(1 - (1 + r)^(-n)) / r],

where:
PV = present value (in this case, $250,000)
Payment = monthly payment
r = monthly interest rate (9% / 12 = 0.0075)
n = number of payments (20 years * 12 months = 240)

Rearranging the formula to solve for Payment, we get:

Payment = PV * r / (1 - (1 + r)^(-n))
Payment = $250,000 * 0.0075 / (1 - (1 + 0.0075)^(-240))
Payment = $2,249.31

Therefore, the monthly benefits will be $2,249.31, paid at the end of each month.

A Retirement Plan Guarantees to Pay to You or Your