Question

Bill has been investing $5,000 for the last 23 years. How much has he accumulated assuming he has earned 7% compounded annually on his investment? Calculate the following scenarios for ordinary annuity.

You are going to receive $205,000 in 18 years. What is the difference in present value between using a discount rate of 15 percent versus 9 percent?

Answer 1

a.Future value of annuity=Annuity[(1+rate)^time period-1]/rate

=5000*[(1.07)^23-1]/0.07

=5000*53.4361409

=$267180.70(Approx)

b.At 15%:

Present value=205000*Present value of discounting factor(rate%,time period)

=205000/1.15^18

=205000*0.0808051189

=16565.0494(Approx)

At 9%:

Present value=205000*Present value of discounting factor(rate%,time period)

=205000/1.09^18

=205000*0.21199374

=43458.7167(Approx)

Hence difference=43458.7167-16565.0494

=$26893.67(Approx)