Question

You just won the lottery, which promises you $200,000 per year for the next 20 years. You receive the first payment today (hint: annuity due). If your discount rate is 9.25%, what is the present value of your winnings?

Answer 1

The present value of the lottery winnings, provided as an annuity due, is calculated using the formula for an annuity due, taking into account the $200,000 annual payments, a discount rate of 9.25%, and a total of 20 years of payments.

Step-by-step explanation:

The question involves calculating the present value of lottery winnings given as an annuity due. An annuity due is a series of payments received at the beginning of each period. Since the first payment is received today, the present value calculation is slightly different from an ordinary annuity, where payments are received at the end of each period.

The discount rate is an interest rate used to determine the present value of future cash flows. To calculate the present value of the lottery winnings, we use the formula for an annuity due, which is PV = Pmt × [(1 - (1 + r)^-n) / r] × (1 + r), where Pmt is the yearly payment, r is the discount rate per period, and n is the number of periods.

Let's plug in the values:

1. Pmt = $200,000 (annual payment)
2. r = 9.25% or 0.0925 (annual discount rate)
3. n = 20 years

So the present value (PV) calculation is as follows:

PV = $200,000 × [(1 - (1 + 0.0925)^-20) / 0.0925] × (1 + 0.0925)

By performing the calculations, we arrive at the present value of the lottery winnings, which accounts for the discount rate and the fact that payments begin immediately as per the terms of an annuity due.