Tracy won a $100 million jackpot. she can receive the jackpot as a $5 million payment each year for 20 years, or she can ask to receive the present value of all those payments all at once now. assume an annual interest rate of 5 percent. if she decides to take the present value payment, about how much will she receive? a. $52.1 millionb. $71.4 millionc. $62.3 milliond. $78.6 million

C. 62.3 million

Explanation:

This question is testing your knowledge of Annuity. In this particular case, it is testing knowledge of present value of annuity.

Before we proceed to the calculations, it is important to understand how to recognize an annuity and its purpose.

An annuity is a constant, regular, equal stream of cash-flow.

In a question like this, annuity helps us compare and understand if it is more valuable to accept some money now or look to what we will get in the future.

We would like to compare which is more profitable; collecting the $100 million now or collecting $5 million every year for 20 years.

We have to bring the two figures to the same period or base so we can compare. It is easier to bring the value of all the future streams of $5 million down to the present figure and compare with $100 million. We do this using the Present Value of Annuity formula.

P = PMT * [(1 - (1/1+r)^n) / r

Where P = Present Value

      PMT = Constant Equal Stream of Cashflow

           r  = Rate

and n     = Number of periods or years

In the question, PMT = $5 Million, r = 5%, n = 20 Years

therefore,

P = 5 million * [ (1 - (1/1.05)^20) / .05]

P = 5 Million * [(1 - (0.9524)^20) / .05]

P = 5 Million * [(1 - (0.3769) / 0.05]

P = 5 Million * [ (0.6231 / 0.05) ]

P = 5 Million * (12.4622)

P = 62.3 Million

I hope the step by step process really helps you.

c

explanation:

answer; automated fingerprint;