## 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.

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}