Question

A $1,000,000 lottery prize pays $50,000 per year for the next 20 years. If the current rate of return is 3.75%, what is the present value of this prize. (Assume the lottery pays out as an ordinary annuity. Round your answer to the nearest cent.)

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Answer to a math question A $1,000,000 lottery prize pays $50,000 per year for the next 20 years. If the current rate of return is 3.75%, what is the present value of this prize. (Assume the lottery pays out as an ordinary annuity. Round your answer to the nearest cent.)

Expert avatar
Cristian
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118 Answers
Given:
- Periodic payment amount, P = \$50,000
- Periodic interest rate, r = 3.75\% = 0.0375
- Total number of payments, n = 20 years

The formula for the present value of an ordinary annuity is:
PV = P \times \left(\frac{1 - (1 + r)^{-n}}{r}\right)

Substitute the given values into the formula:
PV = \$50,000 \times \left(\frac{1 - (1 + 0.0375)^{-20}}{0.0375}\right)

Now, let's calculate step by step:

**Step 4: Calculate the discount factor**
(1 + 0.0375)^{-20} \approx 0.4789

**Step 5: Perform the subtraction**
1 - 0.4789 \approx 0.5211

**Step 6: Divide by the interest rate**
\frac{0.5211}{0.0375} \approx 13.8962

**Step 7: Multiply by the payment amount**
\$50,000 \times 13.8962 \approx \$694,810.21

**Step 8: Round to the nearest cent**
The present value of the lottery prize is approximately \$694,810.21.

\therefore The present value of the prize is approximately \$694,810.21.

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