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Twenty years ago, you won a state lottery, and you received $15,000 at the end of each of the next 10 years, and $20,000 at the end of years 11 through 15. Since you did well in FIN 3403, you decided to invest each of your lottery payments. If you earned 9% per year, how much do you have at the end of year 20

Respuesta :

The value of the amount won at the lottery at the end of 20 years is  $723,672.24.

What is the value at the end of 20 years?

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: https://brainly.com/question/24108530

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