Question

Please show formula(s) and work.

5 FUTURE VALUE: ANNUITY VERSUS ANNUITY DUE What's the future value of a 590, 5-year ordinary annuity that pays $800 each year? If this was an annuity due, what would its future value be?

Answer 1

An ordinary annuity is an annuity that is paid/received at the end of each time period. (the time period is years in this case).

An annuity due is an annuity that is paid/received at the beginning of each time period. (the time period is years in this case too).

The formula for calculating the future value of an ordinary annuity is given below:

Future Value of Ordinary Annuity = Annuity amount*[((1+r)^n)-1)/r]

Thus, in the given question the,

Annuity amount = $800

r = 5%

n = 5

Thus, Future Value of Ordinary Annuity = $800*[((1+5%)^5)-1)/5%]

Solving this gives us a Future Value of Ordinary Annuity of $4,420.51

As for Annuity due, one extra period of compounding occurs, as payments are made during the beginning of the year.

Future Value of Annuity due = Future Value of Ordinary Annuity*(1+r)

Thus, Future Value of Annuity Due = $4,420.51*(1.05)

Solving this gives us a Future Value of Annuity due of $4,641.54