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tangare [24]
3 years ago
13

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?
Business
1 answer:
dsp733 years ago
8 0

Answer:

The present value of your winnings is <u>$1,959,555.65</u>.

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 <u>$1,959,555.65</u>.

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Given:

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