Question

Present value of an annuity

On January 1, you win $56,250,000 in the state lottery. The $56,250,000 prize will be paid in equal installments of $6,250,000 over nine years. The payments will be made on December 31 of each year, beginning on December 31 of this year. The current interest rate is 6.5%.

Determine the present value of your winnings. Round your answer to the nearest dollar.

$ _________

Answer 1

Solution:

Here we need to find the present value of annuity payments made at the end of each year for 9 years.

PV of $6,250,000 over nine years @ 6.5% interest = 6,250,000 * PV Annuity Factor @ 6.5% for 9 years = 6,250,000 * 6.656104 = $41600650

Alternatively,

we can use the formula method as follows;

Pmt	$62,50,000	Payments of a fixed amount
i	6.50%	Interest Rate
n	9	no of payment period

Present Value of an Annuity
Formula
Present Value = PMT[1-1/(1+i)^n]/i
1+i	1.0650
(1+i)^n	1.7626
1/(1+i)^n	0.5674
1-1/(1+i)^n	0.4326
[1-1/(1+i)^n / i]	6.6561
Present Value	$4,16,00,651