To determine the maximum consumption Lara Beal can achieve in her old age, we need to evaluate her options for allocating her wealth between saving/lending and investing in the project.
Given Information:
- Current wealth in youth: $8,000
- Interest rate for lending/borrowing: 15% (i.e., $1 lent today yields $1.15 in the future)
- Project investment cost: $5,000
- Project payoff in old age: $6,000
Analysis of Options:
Option 1: Investing in the project
-
If Lara invests in the project, she will spend $5,000 today, leaving her with:
- Remaining cash in youth: $8,000 - $5,000 = $3,000
-
The total amount she will have in old age from the project is $6,000.
-
For her remaining cash of $3,000, if she chooses to lend this amount at the bank:
- Future value of $3,000 at 15% interest:
- FV = $3,000 * (1 + 0.15) = $3,000 * 1.15 = $3,450
-
So the total consumption in old age if she invests in the project and lends her remaining cash would be:
- Total consumption = Payoff from project + Amount from lending = $6,000 + $3,450 = $9,450
Option 2: Not investing in the project
- If Lara decides not to invest in the project, she can lend the entire $8,000 at the bank:
- Future value of $8,000 at 15% interest:
- FV = $8,000 * (1 + 0.15) = $8,000 * 1.15 = $9,200
Conclusion:
Comparing both options:
- Option 1 (Investing in the project and lending remaining cash): $9,450
- Option 2 (Lending the entire $8,000): $9,200
The highest consumption Lara can achieve in her old age is from Option 1.
Maximum consumption in old age: 9450.00