Sally has $3, 000, 000 on deposit in a fund that earns 10% interest compounded annually.How much can Sally withdraw annually from the fund in ten equal annual withdrawals to completely deplete the fund after the tenth draw, assuming the first withdrawal occurs one year from today?
A)$300, 000
B)$443, 851
C)$488, 237
D)$545, 945

Question

Quizplus · Accepted Answer

To determine the annual withdrawal amount, we need to use the present value of an annuity formula. We can calculate the present value of the entire fund after 10 years at the 10% interest rate as follows:

PV = 3,000,000 / (1 + 0.10)^10
PV = 1,220,185.39

Now we can use this present value as the future value of an annuity that pays out over 10 years. Using the formula:

PV = (PMT / r) x [1 - (1 + r)^-n]

Where PV is the present value (1,220,185.39), PMT is the annual withdrawal amount, r is the interest rate (0.10), and n is the number of periods (10).

Solving for PMT:

PMT = (PV x r) / [1 - (1 + r)^-n]
PMT = (1,220,185.39 x 0.10) / [1 - (1 + 0.10)^-10]
PMT = 488,237.06

Therefore, Sally can withdraw $488,237 annually for 10 years to completely deplete the fund after the tenth draw.

The answer is C.

Sally Has $3, 000, 000 on Deposit in a Fund