Question

Jose wants to cash in his winning lottery ticket. He can either receive five $5,000 annual payments starting today, or he can receive a lump-sum payment now based on a 3% annual interest rate. What would be the lump-sum payment?

Answer 1

Answer:

The lump sum payment =  $23,585.49

                                 

Explanation:

The winning lottery is an example of an advanced annuity. An advanced annuity is a series of cash flows that occurs for a certain number of years with the first cash flow occurring now.

The first cash flow is represents one out of the five, so the balance is a four-year annuity.

So we can work out the present value of the annuity for the last four years as follows:

PV = (1 - (1+r)^(-n)/r )   ×  Annual cash flow

r = 3%=0.03, n = 4, Annual cash flow = 5000

PV = (1- ((1+0.03)^(-4))/0.03)  × 5,000

    = 3.7170 × 5,000

   =$ 18,585.49

The lump sum payment = PV of the first payment + PV of the four year annuity

The lump sum payment = $5000 + $ 18,585.49

                                       =  $23,585.49