Question

F1). Sam Hill has just won the state lottery, paying $200,000 a year for the next 30 years. Sam will receive his first payment today. If the interest rate is 5%, what is the present value of his lottery winnings? (Enter a positive value and round to 2 decimals)

Answer 1

Here sam will receive money at beginning of year , hence formula of annuity due will be used

PV(annuity) = A[1-(1/(1+r)^n / r ] x (1+r)

here A = annuity = 200,000 $

r = rate of interest = 5%

n = no. of years = 30 years

thus PV(annuity) = 200,000[1-(1/(1+5%)^30 / 5% ] x (1+5%)

=200000[1-(1/(1+0.05)^30 / 0.05 ] x (1+0.05)

=200,000[1-(1/(1.05)^30 / 0.05] x (1.05)

=200,000[1-0.2314 / 0.05] x 1.05

=200,000[0.7686 / 0.05] x 1.05

=200,000 x 15.37245 x 1.05

=32,28,214.72 $

Thus present value of lottery = 32,28,214.72 $