Question

You won a lottery! To collect your winnings you will be paid annual amounts of $10,900 for each of the next 22 years. The appropriate discount rate is 9 percent per year. Calculate the difference in the present value if you are paid these annual amounts of money at the beginning of each year rather than at the end of each year. (please explain how to calculate on a financial calculator)

A) 11,881

B) 9779

C) 10,900

D) 9,263

E)10,670

Answer 1

Option D $9263

1. Computation of Difference between  present value:

a. Present Value if the annual installments paid at the end of year

Present Value = Annual Installment * PVAF ( 9%, 22Y)

Present Value = 10900 * 9.4424

Present Value = $102922.16

b. Present Value if the annual installments paid at the beginning of year

Present Value = Annual Installment * PVA due factor ( 9%, 22Y)

Present Value = 10900 * 10.2922

Present Value = $112184.98

c. Difference in Present Values = $112184.98 - $102922.16

Difference in Present Values = $9263