To find out how much wealth Lara Beal can consume in her old age, we need to analyze her options regarding lending, borrowing, and the investment project.
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Current Cash: Lara has $8,000 in cash.
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Bank lending: If she lends money at a 15% interest rate, each dollar lent will grow to $1.15 in old age.
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Project Investment: The project costs $5,000 now and yields $6,000 in old age.
Step 1: Considering the investment project
If Lara decides to invest in the project:
- She needs to invest $5,000 now and will receive $6,000 in old age.
- After investing $5,000, she will have $8,000 - $5,000 = $3,000 left for consumption or further lending.
Step 2: Calculating total future consumption
From the project, she will have:
- $6,000 from the project in old age.
If she decides to lend the remaining $3,000 at the bank:
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The amount she will have in old age from lending $3,000 at 15%:
Future value from lending = $3,000 * (1 + 0.15) = $3,000 * 1.15 = $3,450.
Total consumption in old age if she invests in the project:
- Total = Project payoff + Future value from lending = $6,000 + $3,450 = $9,450.
Step 3: Alternative option - Not investing in the project
We should also consider the scenario where Lara does not invest in the project.
In this case, she could simply lend all her current cash of $8,000 at the bank:
- Future value from lending = $8,000 * (1 + 0.15) = $8,000 * 1.15 = $9,200.
Step 4: Comparing the two scenarios
- If Lara invests in the project: She can consume $9,450 in old age.
- If she lends all her cash: She can consume $9,200 in old age.
Conclusion
The maximum amount Lara can consume in her old age is from investing in the project.
Thus, the final answer is:
9,450.00