# What Is The Future Annuity Of 23,000 Per Year, For 3 Years At 10% Interest Compounded Annually?

If payment into the annuity is done at the beginning of the period, and the value is measured at the end of the period, the total value is
\$23,000(1+10%)(1+10%)(1+10%) +
\$23,000(1+10%)(1+10%) +
\$23,000(1+10%) = \$23,000(1+10%)(1 + (1+10%) + (1+10%)(1+10%))
= \$23,000(1.10)(2.10 + 1.21) = \$23,000(1.1)(3.31) = \$83,743
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The amount 23k*1.13 represents the value of the first payment after 3 years; the amount 23k*1.12 represents the value of the second payment after it has been earning interest for 2 years; 23k*1.1 is the value of the final payment after it has earned interest for 1 year. If you have a longer string of payments, there is a formula for figuring this, but it is more complicated than necessary for this problem.
thanked the writer.
Oddman commented
The calculation here is for an "annuity due". Payment is made at the beginning of the period and the value is determined at the end of the period.
Using the Ordinary Annuity Table:

Period=3 years * 1=3 Rate=10% / Annually=10%
\$23,000 * 3.3100=\$76,130

Calculating Manually

End of year 1: \$23,000
year 2: \$23,000 + \$ 2,300 (.10*\$23,000) = \$25,300

End of year 2:+ \$23,000 + (prev. Year bal.) 25,300 = year 3: \$48,300
\$48,300 + \$ 4,830 (.10*\$48,300) = \$53,130

+ \$23,000 + (prev. Year bal.) \$53,130=

End of year 3: \$76,130
thanked the writer.
Oddman commented
The calculation here is for an "ordinary annuity". The value is determined immediately after payment is made.
Anonymous commented
I need to revise my answet Oddman has the correct answer, if I times my value at end of the year period by 10% it would be \$83,743. I apologize for this mistake, two thumbs up Oddman

MsDayeil 