Find the present value of lottery prize

Question

if you won the lottery that paid $5000 each year for the next 10 years and interest rates were 9% compounded annually, what would be the present value of your prize

Answer 1

The regular compound interest formula does not 

work because there are annual deposits.

 

The formula is at : http://www.moneychimp.com/articles/finworks/fmbasinv.htm

 

It is P(1 + r)^t + c[ ((1 + r)^t - 1) / r ]

where P is the starting principal, r is the interest rate, c is the regular deposit, and t is the time.

 

 

For this problem:

  P = c = $5000 , the annual deposit

  r=9%, so 100% + 9% = 109% = 1.09

 t = 10 years

 

5000(1.09)^10 + 5000 ( (1.09)^ 10 - 1.)/.09) = 87801.46