Question

wants to cash in her winning lottery ticket. She can either receive eight $200,000 semiannual payments starting today, based on a 6% annual interest rate, or she can receive a single-amount payment today. What is the single-amount payment she can receive today that would be equivalent to the eight-payment option except that she would not have to wait for years

Answer 1

A sum of $ 1,446,056.59 will be equivalent of the semiannual payment at the given discount rate of 6% annual

Step-by-step explanation:

We need to solve for the present value of a annuity-due (payment at the beginning of the period) of eight payment of $ 200,000 every six month discounted at 6% annual:

`C * (1-(1+r)^(-time) )/(rate)(1+r) = PV\\`

C 200,000

time 8

rate 0.03 (6% is the annual rate we have semiannual payment so we divide by 2; thus 3%)

`200000 * (1-(1+0.03)^(-8) )/(0.03)(1+.03) = PV\\`

PV $1,446,056.5910