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

$102,677.20

Explanation:

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

`PV = P+P*((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*((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.