Question

Chris Quincy wants to withdraw $40,000 each year for 7 years from a fund that earns 15% interest.

How much must he invest today if the first withdrawal is at year-end? How much must he invest today if the first withdrawal takes place immediately? (Round factor values to 5 decimal places, e.g. 1.25124 and final answers to 0 decimal places, e.g. 458,581.)

Answer 1

We need to find out the present value of the amount so that we can determine how much to be invested.

Present value =Withdrawl Amount per year x Present value of an ordinary annuity of $1(PVIF)

PVIF at 15% for 7 years= [1 - (1 + r)^-n] / r

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

n=7 years

r=15/100

=0.15

PVIF at 15% for 7 years=[1 - (1/(1 + r)^n)] / r

=[1 - (1/(1 + 0.15)^7)] / 0.15

=[1 - (1/(1.15)^7)] / 0.15

=[1 - (1/2.66002] / 0.15

=[1 - 0.37594] / 0.15

=0.62406/0.15

=4.1604

Present value = Withdrawl Amount per year x Present value of an ordinary annuity of $1(PVIF)

= $40,000 x 4.1604

= 1,66,416