The $40 million lottery payment that you have just won actually pays $2 million per year for 20 years. The interest rate is 8%.

a. If the first payment comes in 1 year, what is the present value of the winnings?

b. What is the present value if the first payment comes immediately?

We will apply the annuity formula because payments are made equally at year end for 40 years. we would have applied compound formula if total payment was made at year 40.

Total Payment = $40 mill.

Annual Payment = 2 mill.

Total time for payments = 20

Ir = 8%

A)

Present Value of innings applying annuity formula

P=R (1 - (1+i) ^-n) / i

P=2 (1 - (1+8%) ^-20) / 8%

P=2 (1-0.2145) / 8%

P=2*9.8181

P=19.6362

B)

Present Value of innings applying annuity formula with Advance payment

Value of the first payment is same because it is paid at day 1 so present value is same i. e $2 mill.

Present Value of other 19 Payments with 19 years time from today

Applying the same formula

P=R (1 - (1+i) ^-n) / i

P=2 (1 - (1+8%) ^-19) / 8%

P=2 (1-0.2317) / 8%

P=2*9.6035

P=19.207

Present value of 1st payment at Year. 0 = 2 mill

Present value of 19 payment at Year. 0 = 19.207

Total Value = 2+19.207 = $21.02 mill