Approximately how much should be accumulated by the beginning of retirement to provide a $2,500 monthly check that will last for 25 years, during which time the fund will earn 8 percent interest with monthly compounding?
A)$261,500.00
B)$323,800.00
C)$578,700.00
D)$690,000.00 PV = $2,500
= $2,500 [149.925-20.405]
= $2,500 [129.52]

Question

Quizplus · Accepted Answer

We can use the present value formula for an annuity due to calculate the required savings:
PV = PMT x [(1 - (1 + r/n)^-nt) / (r/n)] x (1+r/n)
where PV is the present value, PMT is the monthly payment, r is the annual interest rate, n is the number of compounding periods per year, and t is the total number of periods.
Substituting the given values, we get:
PV = $2,500 x [(1 - (1 + 0.08/12)^(-25*12)) / (0.08/12)] x (1+0.08/12)
PV = $2,500 x 129.515
PV = $323,787.50
So, the required savings at retirement should be approximately $323,800. Therefore, the best choice is B.

Approximately How Much Should Be Accumulated by the Beginning of Retirement