Question

The $30.0 million lottery payment that you have just won actually pays $1.5 million per year for 20 years. The interest rate is 8%. a. If the first payment comes in 1 year, what is the present value of the winnings? (Do not round intermediate calculations. Enter your answer in dollars, not millions, rounded to 2 decimal places.) Present value b. What is the present value if the first payment comes immediately? (Do not round intermediate calculations. Enter your answer in dollars, not millions, rounded to 2 decimal places.) Present value

Answer 1

1)

Present value = Annuity * [1 - 1 / (1 + r)ⁿ] / r

Present value = 1,500,000 * [1 - 1 / (1 + 0.08)²⁰] / 0.08

Present value = 1,500,000 * [1 - 0.214548] / 0.08

Present value = 1,500,000 * 9.818147

Present value = $14,727,221.11

2)

Present value = (1 + r) * Annuity * [1 - 1 / (1 + r)ⁿ] / r

Present value = (1+ 0.08) * 1,500,000 * [1 - 1 / (1 + 0.08)²⁰] / 0.08

Present value = 1.08 * 1,500,000 * [1 - 0.214548] / 0.08

Present value = 1.08 * 1,500,000 * 9.818147

Present value = $15,905,398.80