Question

Consider a lottery that pays to the winner an annual annuity of $96 that begins in one year and continues for 9 consecutive years with one exception -- the payment at the end of year 3 (and only in this year) is not $96 but instead is $144. Using an interest rate of 2%, determine the present value of this prize.

Answer 1

Given, Annual annuity of $96 that begins in one year and continues for 9 consecutive years with one exception -- the payment at the end of year 3 (and only in this year) is not $96 but instead is $144.

Lets us assume it as $96 ordinary annuity and a single payment of $48 at the end of third year.

Using Formula

PV = FV/(1+r)^t & PV = A(1+(1+r)^(-n))/r

For $48, PV = 48/1.02^3 = $45.23

For yearly payment of $96

PV = 96*(1+(1.02^(-9)))/0.02 => PV = 8816.43

Total Present value of prize = 8816.43+45.23 = $8861.63