Question

Tracy won a $100 million jackpot. She can receive the jackpot as a $5 million payment each year for 20 years, or she can ask to receive the present value of all those payments all at once now. Assume an annual interest rate of 5 percent. If she decides to take the present value payment, about how much will she receive

Answer 1

Answer:

Present value payment = 62.3 million (approx)

Explanation:

Given:

Per year amount (PMT) = 5 million

Number of payment (n) = 20 year

Annual interest rate = 5% = 0.05

Present value payment = ?

Computation of Present value payment:

$Present\ value\ payment = PMT[\frac{1-(1+r)^{-n}}{r} ] \\\\Present\ value\ payment = 5 million[\frac{1-(1+0.05)^{-20}}{0.05} ] \\\\Present\ value\ payment = 5 million[\frac{1-(1.05)^{-20}}{0.05} ] \\\\Present\ value\ payment = 5 million[\frac{0.623110517}{0.05} ] \\\\Present\ value\ payment = 5 million[12.4622103]\\\\Present\ value\ payment = 62.3 million$

Present value payment = 62.3 million (approx)