Question

The state​ lottery's million-dollar payout provides for ​$1.21 million to be paid in 20 installments of ​$60,000 per payment. The first ​$60,000 payment is made​ immediately, and the 19 remaining $60,000 payments occur at the end of each of the next 19 years. If 8 percent is the discount​ rate, what is the present value of this stream of cash​ flows? If 16 percent is the discount​ rate, what is the present value of the cash​ flows?

Answer 1

Present value of annuity due= payment per period * [1-(1+i)^-n]/i *(1+i)

i = interest rate per period

n = number of periods

a)

Present value = 60000 * [1-(1+0.08)^-20]/0.08 * 1.08

= 636215.95

b)

Present value = 60000 * [1-(1+0.16)^-20]/0.16 * 1.16

= 412647.33