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

2 Answers

Oddman answered

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
_____
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.

Anonymous answered

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

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

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