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10) supposed state lottery price of 3 million is paid in 25 payments of $120,000 each at the end of each of the next 25 years if the money is worth 12% compounded annually what is the present value of the prize (rounds your answer to the nearest cent)

11) what amount must be set aside now to generate payments of $50,000 at the beginning of each year for the next 12 years if money is worth 6.09% compounded annually (round your answer to the nearest cent)

Answer 1

10. Amount paid at end of each year = P = $120000

Interest Rate = r = 12%

Number of years = n = 25

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

= 120000[1- (1+0.12)^-25]/0.12

= $941,176.69

11. Let the amount set aside be PV

Payment required each year = P = $50000

Number of Years = n = 12

Interest rate = r = 6.09%

Hence, PV = P + P/(1+r) +....+ P/(1+r)^n-1 = P + P[1- (1+r)^-(n-1)]/r

= 50000 + 50000[1- (1+0.0609)^-11]/0.0609

= $ 442,534.89