You are scheduled to receive annual payments of $9,600 for each of the next 22 y
ID: 2773759 • Letter: Y
Question
You are scheduled to receive annual payments of $9,600 for each of the next 22 years. Your discount rate is 8 percent. What is the difference in the present value if you receive these payments at the beginning of each year rather than at the end of each year?
You are scheduled to receive annual payments of $9,600 for each of the next 22 years. Your discount rate is 8 percent. What is the difference in the present value if you receive these payments at the beginning of each year rather than at the end of each year?
Explanation / Answer
Present value if payment is received at the end of the year Cash Flow Discount Present value 1 9600 0.925926 8888.889 2 9600 0.857339 8230.453 3 9600 0.793832 7620.79 4 9600 0.73503 7056.287 5 9600 0.680583 6533.599 6 9600 0.63017 6049.628 7 9600 0.58349 5601.508 8 9600 0.540269 5186.581 9 9600 0.500249 4802.39 10 9600 0.463193 4446.657 11 9600 0.428883 4117.275 12 9600 0.397114 3812.292 13 9600 0.367698 3529.9 14 9600 0.340461 3268.426 15 9600 0.315242 3026.32 16 9600 0.29189 2802.148 17 9600 0.270269 2594.582 18 9600 0.250249 2402.391 19 9600 0.231712 2224.436 20 9600 0.214548 2059.663 21 9600 0.198656 1907.095 22 9600 0.183941 1765.829 Present Value 97927.14 Present value if payment is received at the beginning of the year Cash Flow Discount Present value 1 9600 1 9600 2 9600 0.925926 8888.889 3 9600 0.857339 8230.453 4 9600 0.793832 7620.79 5 9600 0.73503 7056.287 6 9600 0.680583 6533.599 7 9600 0.63017 6049.628 8 9600 0.58349 5601.508 9 9600 0.540269 5186.581 10 9600 0.500249 4802.39 11 9600 0.463193 4446.657 12 9600 0.428883 4117.275 13 9600 0.397114 3812.292 14 9600 0.367698 3529.9 15 9600 0.340461 3268.426 16 9600 0.315242 3026.32 17 9600 0.29189 2802.148 18 9600 0.270269 2594.582 19 9600 0.250249 2402.391 20 9600 0.231712 2224.436 21 9600 0.214548 2059.663 22 9600 0.198656 1907.095 Present Value 105761.3 Difference = Present Value of annuity beginning- Present Value of annuity due = 105761-97927 = 7834
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