Jesse has just learned that she won $1 million in her state lottery. She has the choice of...

Question:

Jesse has just learned that she won $1 million in her state lottery. She has the choice of receiving a lump-sum payment of $312,950, or $50,000 per year, for the next 20 years. Jesse can invest the lump sum at 8%, or she can invest the annual payments at 6%. Which should she choose for the greatest return, after 20 years?

Lottery Payments:

Lottery payments are usually not paid out as advertised and are paid out as either a number of payments over the years as advertised or a lumpsum which is much less than what is advertised.

Answer and Explanation:


The $50,000 payments are better


We can calculate the present value of the payments over the 20 years and compare with the given lumpsum payment:

{eq}PV= Payment\times \dfrac{1-(1+r)^{-n}}{r} {/eq}

Here:

  • Present value (PV) shall be the value of $50,000 payments.
  • Payment = $50,000
  • r (rate) = 6% or 0.06. This is the same rate as the investment rate.
  • n = 20

Substituting the values we have:

{eq}Present\:Value = P \times \dfrac{1-(1+0.06)^{-20}}{0.06} {/eq}

{eq}Present\:Value = $50,000 \times 11.46992122 {/eq}

{eq}Present\:Value = $573,496.06 {/eq}


Learn more about this topic:

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How to Find the Value of an Annuity

from Algebra II Textbook

Chapter 21 / Lesson 15
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