Question

A. You have just been notified that you will receive  $8,800 a year for the next 18 years from an inherited trust. If the interest rate is 13 percent, how much should you be willing to accept today in exchange for the annual payments? (Enter your answer as a positive number rounded to 2 decimal places.)

B. You just won the $41 million lottery. You will receive $2.1 million a year for the next 15 years plus an additional payment of $9.5 million at the end of 15 years. The interest rate is 8 percent. How much is your lottery prize worth today? (Enter your answer as a positive number rounded to 2 decimal places.)

C. Your aunt offers you a choice of $21,600 in 30 years or $200 today. At a discount rate of 17 percent, how much is your aunt's offer of $21,600 worth today? (Enter your answer as a positive number rounded to 2 decimal places.)

D. Sherwin Williams will earn $18,250 a year for the next 15 years for a picture he has painted. At an interest rate of 7 percent, how much are the earnings worth today? (Enter your answer as a positive number rounded to 2 decimal places.)

Answer 1

A) In this case we need to calculate the present value of annual payments which is shown as follows:-

Present Value = Annual Payments*PVAF(13%, 18 yrs)

= $8,800*6.83991 = $60,191.21

Hence I will be willing to accept $60,191.21 today in exchange for the annual payments.

B) Present Worth of Lottey prize = [Annual receipts*PVAF(8%, 15 yrs)]+[Additional Payment*PVF((8%, 15 yrs)]

= ($2,100,00920*8.55948)+($9,500,000*0.31524)

= $17,974,908+$2,994,780 = $20,969,688

Hence the present worth of lottery prize is $20,969,688.

C) Worth of Aunt's offer = $21,600*PVF(30 yrs, 17%)

= $21,600*0.00900376489 = $194.48

D) Worth of his earnings = Annual earning*PVAF(15 yrs, 7%)

= $18,250*9.10791 = $166,219.36