Question

You have won the lottery and will receive 20 annual payments of $10,000 starting today. If you can invest these payments at 8.5%, what is the present value of your winnings?

Answer 1

Answer:

$102,677.20

Step-by-step explanation:

The present value of an annuity due is determined by the following expression:

$PV = P+P*(\frac{1-(1+r)^{-n+1}}{r})$

Where 'P' is the amount of each payment received, 'r' is the interest rate on the investment and 'n' is the number of yearly payments.

With 20 annual payments of $10,000 at a rate of 8.5%, the present value is:

$PV = 10,000+10,000*(\frac{1-(1+0.085)^{-20+1}}{0.085})\\PV = 10,000+ 10,000*(9.26772)\\PV=\ 102,677.20$

The present value of your winnings is $102,677.20.