Go to the Student Edition of the textbook’s Web site. In Chapter 10, find “Influence of Annuity Variables.” This interactive chart enables you to observe and compare the effects of changes in the variables PMT, n, and i on both the future value and present value of an annuity.
a. Enter PMT = $100 and I = 8% for both Annuity A and Annuity B. Set n = 20 for Annuity A and n = 40 for Annuity B. This means that B contains twice as many payments as A. In percentage terms,
(i) How much larger is the present value of B than the present value of A?
(ii) How much larger is the future value of B than the future value of A?
b. Enter PMT = $100 and n = 30 for both annuities. Set I = 8% for Annuity A and i = 9% for Annuity B. In relative terms, the interest rate for B is
9% - 8% / 8% × 100% = 12.5%
larger than the rate for A. In percentage terms,
(i) How much smaller is the present value of B than the present value of A?
(ii) How much larger is the future value of B than the future value of A?