Question

Beginning three months from now, you want to be able to withdraw $4,100 each quarter from your bank account to cover college expenses over the next four years. If the account pays .81 percent interest per quarter, how much do you need to have in your bank account today to meet your expense needs over the next four years?

Answer 1

Answer:

The answer is$61,294.59

Explanation:

To solve this problem, we will need to calculate the Present value of annuity , which is the money required in the bank today. The formula is given as:

Present value of annuity  = Annuity x PVAF

where:

Annuity = Quarterly withdrawal = $4,100

PVAF = Present value annuity factor = $\frac{1-(1+r)^-^{n} }{r}$

where:

r = periodic rate = 0.0081

n = number of periods = 4 X 4 = 16 quarters

we calculate for PVAF thus:

=> $\frac{1-(1+0.0081)^-^{16} }{0.0081}$

=> 14.9499

Now, to calculate the Present value of annuity , recall:

=> Annuity x PVAF

=> $4,100 X 14.9499

=> $61,294.59