Question

2. Gabrielle just won $1.8 million in the state lottery. She is given the option of receiving a total of S900,000 now, or she can elect to be paid $90,000 at the end of each of the next 20 years. If Gabrielle can earn 6% annually on her investments, from a strict economic point of view which option should she take? If Gabrielle takes the prize as an annuity, the present value of the 20-year ordinary annuity is S Round to the nearest dollar.) 1,032,293 tprese s Round to the nearest dollar.) Which alternative should be chosen? (Select the best answer below.) O A. Lump sum payment O B. Annuity payments

Answer 1

Present Value of 20-Year Ordinary Annuity

Present Value of 20-Year Ordinary Annuity = P x [{1 - (1 / (1 + r) ⁿ} / r]

= $90,000 x [{1 - (1 / (1 + 0.06) ²⁰} / 0.06]

= $90,000 x [{1 – (1 / 3.20713)} / 0.06]

= $90,000 x [{1 - 0.31180} / 0.06]

= $90,000 x 11.46992

= $10,32,293

“The Present Value of 20-Year Ordinary Annuity = $10,32,293”

Present Value of the Lump Sum Payment

Present Value of the Lump Sum Payment would be $900,000 [ie, the total value of the amount received now]

“Present Value of the Lump Sum Payment = $900,000”

Alternative to be choosen

Gabrielle should choose the “(B). Annuity Payment Method”, Since the Present Value of the future cash payment is higher in Annuity Method, therefore, the annuity method should be selected,