Question

A local government is about to run a lottery, but does not want to be involved in the payoff if a winner picks an annuity payoff. The government contracts with a trust to pay the lump-sum payout to the trust and have the trust (probably a local bank) pay the annual payments. The first winner of the lottery chooses the annuity and will receive $150,000 a year for the next twenty-five years. The local government will give the trust S2,000,000 to pay for this annuity. What investment rate must the trust earn to break even on this arrangement?

Please explain using calculations thank you

Answer 1

Present Value of the Award = PV = $2000000

Annuity Received each year = P = $25000

Number of Years = n = 25

Let the rate of return be r

Present Value of all Annuity PV = P/(1+r) + P/(1+r)² +....+ P/(1+r)ⁿ = P[1- (1+r)^-n]/r

=> 2000000 = 150000[1- (1+r)^-25]/r

=> [1- (1+r)^-25]/r = 13.33

Using hit and trial, we get r = 5.56%