Question

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%.

Answer 1

Answer:

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 = $(1 + \frac{i}{n})^n - 1$

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

Present value of annuity due =

$(1 + 0.06) \times 150 \times (\frac{1 - \frac{1}{(1 + 0.06)^3} }{0.06} )$

= 1.06 $\times$ $400.95

= $425.0089

Present value of ordinary annuity = $150 \times (\frac{1 - \frac{1}{(1 + 0.06)^3} }{0.06} )$

= $150 $\times$ 2.6730

= $400.95

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

Statement a. is correct.