Question

Suppose that you will receive annual payments of $12,500 for a period of 10 years. The first payment will be made 9 years from now. If the interest rate is 6%, what is the present value of this stream of payments? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

Annual Payments = P = $12,500

n = 18 years

x = payment = 8 years

r = interest rate = 6%

Present Value of this stream of payments = [P * [1 - (1+r)^-(n-x)] / r] / (1+r)^x

= [$12,500 * [1 - (1+6%)^-(18-8)] / 6%] / (1+6%)^8

= [$12,500 * 0.441605223 / 0.06] / 1.59384807

= [$92,001.0882] / 1.59384807

= $57,722.6211

Therefore, present Value of this stream of payments is $57,722.62

Calculation of Present Value of Cash Flow Stream
Year	Cash Flow	Discount Factor@6%	Discounted Cash Flows
A	B	C =(1+6%)^-A	D = B*C
9	12,500	0.591898464	7398.730794
10	12,500	0.558394777	6979.934711
11	12,500	0.526787525	6584.844067
12	12,500	0.496969364	6212.117045
13	12,500	0.468839022	5860.487778
14	12,500	0.442300964	5528.762055
15	12,500	0.417265061	5215.813259
16	12,500	0.393646284	4920.578546
17	12,500	0.371364419	4642.055232
18	12,500	0.350343791	4379.297389
Present value of Cash Flow stream			57722.62088