Question

Suppose that you will receive annual payments of \$12,500 for a period of 10 years. The...

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.)

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

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