Question

Which of these is true? The future value of a 10-year, $100 annuity due is always greater than the future value of a 10-year. $100 ordinary annuity with identical risk. The main difference between a 10-year, $100 annuity due and a 10-year, $100 ordinary annuity is the level of risk There is not enough information to compare these two annuities. The future value of a 10-year, $100 annuity due is always less than the future value of a 10-year, $100 ordinary annuity with identical risk.

Answer 1

Correct option is (a) i.e. The future value of a 10-year, $100 annuity due is always greater than the future value of a 10-year,$100 ordinary annuity with identical risk.

Two kinds of annuities depending on the timings of cash flow are classified as ordinary annuity/regular annuity/deferred annuity and annuity due. Ordinary annuity are those annuities in which the cash flows occur at the end of each period. In case of annuity due, the cash flows occur at the beginning of each period.

Since in the annuity due, cash flows occur at the beginning of each period hence compounding takes place for 1 extra year, hence future value of annuity due is always greater than future value of ordinary annuity.

It can further be justified as under:

Future value of annuity (ordinary) = Annuity x Compound value annuity factor

Future value of annuity (due) = Future value of annuity (ordinary) x (1 + r)

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