Question

Suppose you are going to receive $14,000 per year for 9 years. The appropriate interest rate is 10 percent. a. What is the present value of the payments if they are in the form of an ordinary annuity? b. What is the present value if the payments are an annuity due?

Answer 1

Answer;

Part 1

Present value of annuity factor (PVAF)=

formula;

PVAF = PMT[ 1 - 1/(1+R)^n] / R

PMT = periodic payment

PV= present value

R = Rate

n = number of payment

Present value = $14000[ 1 - 1/(1+10%)^9] /10%

= $14000 x 5.759

= $80,626.33 or $80,626

cross check;

Part 2

Present value of due annuity factor (PVAF due )=

formula;

PVAF due = PMTx (1+R) x [ 1 - 1/(1+R)^n] / R

PMT = periodic payment

PV= present value

R = Rate

n = number of payment

Present value = $14000x(1+10%) X [ 1 - 1/(1+10%)^9] /10%

= $15400 x 5.759

= $88,688.97 or $88,689

cross check;