A U.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?
A) The PV of the $1,000 lump sum has a smaller present value than the PV of a 3-year, $333.33 ordinary annuity.
B) The periodic interest rate is greater than 3%.
C) The periodic rate is less than 3%.
D) The present value would be greater if the lump sum were discounted back for more periods.
E) The present value of the $1,000 would be larger if interest were compounded monthly rather than semiannually.

Question

Quizplus · Accepted Answer

The present value of a lump sum payment is lower than the present value of an annuity payment because the annuity payment is spread out over time and therefore subject to less discounting. In other words, the lump sum payment must be discounted more heavily to bring it back to its present value. Therefore, A is the correct choice.

B is incorrect because the nominal rate is 6%, which is an annual rate. The periodic rate is half of that, or 3%.

C is incorrect because the periodic rate is 3%.

D is incorrect because discounting the lump sum back for more periods would only result in a lower present value.

E is incorrect because compounding more frequently would only result in a higher present value if the nominal rate remained the same. In this case, the nominal rate is fixed at 6% and the periodic rate is already semiannual, so compounding more frequently would not change the present value.

A USTreasury Bond Will Pay a Lump Sum of $1,000 Exactly