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

Answer:

The present value of your winnings is $1,959,555.65.

Explanation:

Since  this is an annuity due as already hinted in the question, the formula for calculating the present value (PV) of an annuity is used as follows:

PV = P × [{1 - [1 ÷ (1 + r)]^n} ÷ r] × (1 + r) .................................. (1)

Where ;

PV = Present value of winnings =?

P = Annual payment = $200,000

r = interest rate = 9.25%, or 0.0925

n = number of years = 20

Substituting the values into equation (1) above, we have:

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

PV = 200,000 ×8.96821807613347 × 1.0925

PV = $1,959,555.65

Therefore, the present value of your winnings is $1,959,555.65.