A lottery prize worth $1,000,000 is awarded in payments of $10,000 five times a year for 20 years. Suppose the money is worth 20% compounded five times per year.
What is the formula used to find the present value of the prize?
i = .20/5 = .04
n = 20x5 = 100
PV = 10 000(1 - 1.04^-100)/.04
= 245 049.99
20% interest!!! Wow, what fantasy place is this?
To find the present value of the prize, we need to use the formula for the present value of an annuity. An annuity is a series of equal payments received or made over a period of time. The formula for the present value of an annuity is:
PV = (PMT × (1 - (1 + r)^(-n))) / r
Where:
PV = Present value of the annuity
PMT = Amount of each payment
r = Interest rate per period
n = Number of periods
In this case, the amount of each payment is $10,000 and the interest rate per period is 20% compounded five times per year. The number of periods is 20 (since there are 20 years and 5 payments per year).
So the formula to find the present value of the prize would be:
PV = ($10,000 × (1 - (1 + 0.20/5)^(-5*20))) / (0.20/5)
Now, let's calculate the present value.