Answer:
The lump sum payment = $23,585.49
Explanation:
The winning lottery is an example of an advanced annuity. <em>An advanced annuity is a series of cash flows that occurs for a certain number of years with the first cash flow occurring now.</em>
The first cash flow is represents one out of the five, so the balance is a four-year annuity.
So we can work out the present value of the annuity for the last four years as follows:
PV = (1 - (1+r)^(-n)/r ) × Annual cash flow
r = 3%=0.03, n = 4, Annual cash flow = 5000
PV = (1- ((1+0.03)^(-4))/0.03) × 5,000
= 3.7170 × 5,000
=$ 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
