Your grandmother just died and left you $100,000 in a trust fund that pays 6.5% interest.You must spend the money on your college education,and you must withdraw the money in 4 equal installments,beginning immediately.How much could you withdraw today and at the beginning of each of the next 3 years and end up with zero in the account?
A)$24,736
B)$26,038
C)$27,409
D)$28,779
E)$30,218

Question

Quizplus · Accepted Answer

To find out the amount that can be withdrawn at the beginning of each year, we need to use the present value of an annuity formula.

The formula for calculating the present value of an annuity is:

PV = Pmt x (1 - (1 + r/n)^(-nt)) x (n/r)

Where: 
PV = present value 
Pmt = payment amount 
r = annual interest rate 
n = number of compound periods per year 
t = total number of years

In this case, we can calculate the payment amount (Pmt) as follows:

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

Where PV is the total amount in the trust fund, which is $100,000.

n = 1 (since it's compounded annually)
r = 0.065 (annual interest rate)
t = 4 (payment period)

Pmt = $27,409

Therefore, you can withdraw $27,409 at the beginning of each of the next 4 years (including today) to use up the entire trust fund and end up with zero in the account.

Option C is the correct answer.

Your Grandmother Just Died and Left You $100,000 in a Trust