The value of the amount won at the lottery at the end of 20 years is $723,672.24.
<h3>What is the value at the end of 20 years?
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The formula for calculating future value of annuities is: yearly amount x annuity factor
Annuity factor = {[(1+r)^n] - 1} / r
Where:
- r = interest rate
- n = number of years
Annuity factor for the first ten years = [(1.09^10) - 1] / 0.09 = 15.19293
15.19293 x $15,000 = $227,893.95
Annuity factor for the last 5 years = [(1.09^5) - 1] / 0.09 = 5.9847
5.9847 x 20,000 = $119,694.21
Future value of the lump sum of $227,893.95 in 10 years = $227,893.95 x (1.09^10) = 539,507.86
Future value of the lump sum of $119,694.21 in 5 years = $119,694.21 x (1.09^5) = $184,164.38
Value in year 20 = $184,164.38 + 539,507.86 = $723,672.24
To learn more about annual annuities, please check: brainly.com/question/24108530
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