Question

You just won the florida lottery. To receive the winnings, you must select one of the two following choices
1. You can receive $1.000.000 a year at the end of each of the next 30 years
2. You can receive a one-time payment of $15.000.000 today, assume that the current interest rate is 6% wich opsition is most valuabe?

Answer 1

To determine which option is more valuable, we need to calculate the present value (PV) of the annuity option (Option 1) and compare it to the lump-sum payment (Option 2).

### Option 1: Annuity of $1,000,000 per year for 30 years

The present value of an annuity can be calculated using the formula:

\[
PV = C \times \left( \frac{1 - (1 + r)^{-n}}{r} \right)
\]

Where:
- \(C\) = Cash flow per period ($1,000,000)
- \(r\) = Interest rate (6% or 0.06)
- \(n\) = Number of periods (30 years)

Plugging in the values:

\[
PV = 1,000,000 \times \left( \frac{1 - (1 + 0.06)^{-30}}{0.06} \right)
\]

Calculating \( (1 + 0.06)^{-30} \):

\[
(1 + 0.06)^{-30} = (1.06)^{-30} \approx 0.1741
\]

Now, substitute that value back into the formula:

\[
PV = 1,000,000 \times \left( \frac{1 - 0.1741}{0.06} \right)
\]
\[
= 1,000,000 \times \left( \frac{0.8259}{0.06} \right)
\]
\[
= 1,000,000 \times 13.765
\]
\[
= 13,765,000
\]

### Option 2: Lump-sum payment of $15,000,000 today

This is straightforward since it's a one-time payment with no discounting necessary. It's simply $15,000,000.

### Conclusion

- Present Value of Option 1 (Annuity) = $13,765,000
- Present Value of Option 2 (Lump Sum) = $15,000,000

**Since $15,000,000 > $13,765,000, the one-time payment of $15,000,000 today is the more valuable option.**