S.Treasury bond will pay a lump sum of $1, 000 exactly 3 years from today.The nominal interest rate is 6%, semiannual compounding.Which of the following statements is CORRECT?

Question

Quizplus · Accepted Answer

The present value of a lump sum decreases as the compounding periods increase, and increases as the discount rate decreases. Therefore, if the nominal interest rate is 6%, semiannual compounding, the periodic interest rate is 3% (6% / 2), and the present value of a $1,000 lump sum to be received in 3 years is $839.62. On the other hand, the present value of a 3-year, $333.33 ordinary annuity with a periodic interest rate of 3% is $930.99, which is greater than the present value of the lump sum. Therefore, statement A is correct. Statement B is false because the periodic interest rate is 3%, not greater than 3%. Statement C is false because the periodic interest rate is 3%, not less than 3%. Statement D is false because the present value would be smaller, not greater, if the lump sum were discounted back for more periods. Statement E is false because the present value of the lump sum is not affected by the frequency of compounding as long as the nominal rate and the time period are the same.

STreasury Bond Will Pay a Lump Sum of $1, 000