Question

You are comparing two annuities. Annuity A pays $100 at the end of each month for 10 years. Annuity B pays $100 at the beginning of each month for 10 years. The rate of return on both annuities is 8 percent. Which one of the following statements is correct given this information?
A) The future value of Annuity A is greater than the future value of Annuity B.
B) Annuity B will pay one more payment than Annuity A will.
C) Annuity A has a higher future value but a lower present value than Annuity B.
D) Annuity B has both a higher present value and a higher future value than Annuity A.
E) The present value of Annuity A is equal to the present value of Annuity B.

Answer 1

Answer:

D) Annuity B has both a higher present value and a higher future value than Annuity A

Explanation:

An annuity which pays a fixed sum at the beginning of the period for a number of years is referred to as Annuity Due.

Whereas, an annuity that pays a fixed sum at the end of a period for a number of years is called Deferred Annuity.

Present value of an annuity due is given by:

Present Value = Amount × $\frac{1\ -\ (\frac{1}{(1\ +\ r)^{n} }) }{r}$ × (1 + r)

In case of an annuity due, the present value would be more since no discounting is required for the first installment and secondly since the number of years of installments get reduced by 1 unlike in the case of a deferred annuity.

Future Value = Amount of annuity (in case of equal amounts )× Cumulative annuity factor at r% invested for n years.

Thus, in the given case, Annuity B will have both higher present value and a higher future value.