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. An investment that has a nominal rate of 6% with semiannual payments will have an effective rate that is smaller than 6%.

c. If a loan has a nominal annual rate of 8%, then the effective rate can never be greater than 8%.

d. The proportion of the payment that goes toward interest on a fully amortized loan increases over time.

e. If a loan or investment has annual payments, then the effective, periodic, and nominal rates of interest will all be different.

Answer 1

Suppose interest rate is 6%

Present value of annuity due = (1 + r) * Annuity * [1 - 1 / (1 + r)ⁿ] / r

Present value of annuity due = (1 + 0.06) * 150 * [1 - 1 / (1 + 0.06)³] / 0.06

Present value of annuity due = 1.06 * 150 * 2.673012

Present value of annuity due = 425.01

Present value of ordinary annuity = Annuity * [1 - 1 / (1 + r)ⁿ] / r

Present value of ordinary annuity = 150 * [1 - 1 / (1 + 0.06)³] / 0.06

Present value of ordinary annuity = 150 * 2.673012

Present value of ordinary annuity = 400.95

Present value of annuity due will always be greater than ordinary annuity because there is one less period to discount since payments are made at the beginning of the periods in annuity due.

a. The present value of a 3-year, $150 annuity due will exceed the present value of a 3-year, $150 ordinary annuity