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
4.7
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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