Gabrielle just won ​$3.6 million in the state lottery.  She is given the option of receiving a of ​$1 comma 400 comma 000 ​now, or she can elect to receive ​$120 comma 000 at the end of each of the next 30 years.  If Gabrielle can earn 8​% annually on her​ investments, which option should she​ take?

To determine which option Gabrielle should take, we need to compare the present value (PV) of the two options: 

1. **Option 1:** $1,400,000 now.
2. **Option 2:** $120,000 per year for 30 years at 8% interest.

We calculate the present value of Option 2 using the formula for the present value of an annuity:

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

Where:
- $ P = 120,000 $ (the annual payment),
- $ r = 0.08 $ (the annual interest rate),
- $ n = 30 $ (the number of years).

Let me calculate the present value for Option 2.The present value of Option 2 (receiving $120,000 annually for 30 years) is approximately $1,350,934.

### Comparison:
- **Option 1**: $1,400,000 now.
- **Option 2**: Present value of $1,350,934.

Since Option 1 ($1,400,000) is higher than the present value of Option 2 ($1,350,934), Gabrielle should take the lump sum of $1,400,000 now.

Would you like more details on the calculation or have any further questions?

Here are some related questions:
1. How does the interest rate affect the present value of an annuity?
2. What happens if the interest rate were different, say 6% instead of 8%?
3. How would the decision change if Gabrielle's investment opportunities changed?
4. What is the effect of inflation on long-term payments like annuities?
5. How can Gabrielle maximize her investment if she takes the lump sum?

**Tip**: Always compare the present value of different payment options when making financial decisions.

Gabrielle just won ​$3.6 million in the state lottery. She is given the option of receiving ​$1,400,000 ​now, or she can elect to receive ​$120,000 at the end of each of the next 30 years. If Gabrielle can earn 8​% annually on her investments, which option should she take?

Discover how to compare a lump sum of $1,400,000 now against receiving $120,000 annually for 30 years at an 8% interest rate. Learn about the present value of annuities and make informed financial decisions. Ideal for students studying financial mathematics.

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