Question

You won a lottery! To collect your winnings you will be paid annual amounts of $11,300 for each of the next 21 years. The appropriate discount rate is 10 percent per year. Calculate the difference in the present values if you are paid these annual amounts of money at the beginning of each year rather than at the end of each year.

Answer 1

Difference = $9773.02

Step-by-step explanation:

An annuity is a series of cash flows or payments that are of constant amount, occur after equal intervals of time and are for a limited and defined period of time. Thus, the winnings from lottery are an annuity as they pay a fixed amount $11300 every year for 21 years.

The annuity can be of two types namely ordinary annuity and annuity due. In ordinary annuity the cash flows occur at the end of the period and in annuity due, the cash flows occur at the beginning of the period. When we calculate the present value of these cash flows, it is understood that the present value of annuity due is greater than the present value of ordinary annuity.

The formulas for the present value of both ordinary annuity and annuity due are attached.

In the formula, R is the annuity payment or cash flow and i is the relevant interest rate and n is the number of years or periods.

PV of annuity ordinary = 11300 * [ (1 - (1+0.1)^-21) / 0.1 ]

PV of ordinary annuity = $97730.24548 rounded off to $97730.25

PV of annuity due = 11300 * [ (1 - (1+0.1)^-21) / 0.1 ] * (1+0.1)

PV of annuity due = $107503.27

Difference = 107503.27 - 97730.25

Difference = $9773.02