Which of the following statements is CORRECT?
A) an investment that has a nominal rate of 6% with semiannual payments will have an effective rate that is smaller than 6%.
B) the present value of a 3-year, $150 annuity due will exceed the present value of a 3-year, $150 ordinary annuity.
C) if a loan has a nominal annual rate of 8%, then the effective rate can never be greater than 8%.
D) if a loan or investment has annual payments, then the effective, periodic, and nominal rates of interest will all be different.
E) the proportion of the payment that goes toward interest on a fully amortized loan increases over time.

Question

Quizplus · Accepted Answer

An annuity due has cash flows at the beginning of each period, whereas an ordinary annuity has cash flows at the end of each period. This means that the present value of an annuity due will always be greater than the present value of an ordinary annuity of the same amount and duration. Therefore, statement B is correct.

Statement A is incorrect because the effective rate on an investment with semiannual payments will be greater than 6%, not smaller.

Statement C is incorrect because the effective rate can be greater than the nominal rate if the compounding periods are more frequent than once per year.

Statement D is incorrect because if a loan or investment has annual payments, then the effective, periodic, and nominal rates will be the same.

Statement E is incorrect because the proportion of the payment that goes toward interest on a fully amortized loan decreases over time.

Which of the Following Statements Is CORRECT