Which of the following statements is correct? a. the present value of a 3-year, $150 annuity due will exceed the present value of a 3-year, $150 ordinary annuity. b. if a loan has a nominal annual rate of 8%, then the effective rate can never be greater than 8%. c. if a loan or investment has annual payments, then the effective, periodic, and nominal rates of interest will all be different. d. an investment that has a nominal rate of 6% with semiannual payments will have an effective rate that is smaller than 6%.

Statement a. is correct.

Explanation:

The effective annual rate is always higher than the nominal interest rate, as the formula is clear for any number of periods, for any interest rate:

Effective Annual Rate of return =

Further if we calculate the present value of annuity due and ordinary annuity assuming 6 % interest rate, then:

Present value of annuity due =

= 1.06 $400.95

= $425.0089

Present value of ordinary annuity =

= $150 2.6730

= $400.95

Therefore, value of annuity due is more than value of ordinary annuity.

Statement a. is correct.

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