Ordinary Annuity

Future Values of Equal Cashflows Paid at the End of Each Period

Suppose you are retired and will receive $20,000 at the end of every year for ten years. You would like to understand what is going to be the future value of your money flows at the end of 10 years. The annual interest rate is 5%.


This example above is the ordinary annuity, a series of regular payments made at the end of each period; in this example, it is the year.

Below you can find the formula for calculating the future values of equal cash flows paid at the end of each period or the ordinary annuity:

FV_{N} = A (1 + r)^{N-1} + A (1 + r)^{N-2} + A (1 + r)^{N-3} + .... + A (1 + r)^{1} + A (1 + r)^{0}
FV_{N} = A [(1 + r)^{N-1} + (1 + r)^{N-2} + (1 + r)^{N-3} + .... + (1 + r)^{1} + (1 + r)^{0}]
FV_{N} = A [\frac{(1+r)^{N} - 1}{r}]

Now it is time to apply the above formula to your case:

FV_{N} = \$20,000 (1 + 0.05)^{9} + \$20,000 (1 + 0.05)^{8} + \$20,000 (1 + 0.05)^{7}+ \$20,000 (1 + 0.05)^{6}+ \$20,000 (1 + 0.05)^{5}+ \$20,000 (1 + 0.05)^{4}+ \$20,000 (1 + 0.05)^{3}+ \$20,000 (1 + 0.05)^{2}+ \$20,000 (1 + 0.05)^{1}+ \$20,000 (1 + 0.05)^{0}
FV_{N} = \$20,000 [(1 + 0.05)^{9} + (1 + 0.05)^{8} + (1 + 0.05)^{7}+ (1 + 0.05)^{6}+ (1 + 0.05)^{5}+ (1 + 0.05)^{4}+ (1 + 0.05)^{3}+ (1 + 0.05)^{2}+ (1 + 0.05)^{1}+ (1 + 0.05)^{0}
FV_{N} = \$20,000 [\frac{(1+ 0.05)^{10} - 1}{0.05}]
FV_{N} = \$20,000 [\frac{(1.05)^{10} - }{0.05}]
FV_{N} = \$20,000 [\frac{0.62889}{0.05}]
FV_{N} = \$20,000 \times 12.5778
FV_{N} = \$251,556

The future value of $20,000, paid at the end of every year for ten years with a yearly interest of 5%, will equal $251,556 in 10 years.

If you like this post you may find useful buying this book:

Advertisements

Leave a Reply

Related Posts

Discover more from Cenk Yildiran

Subscribe now to keep reading and get access to the full archive.

Continue reading