Lara Beal allocates wealth between youth and old age. Currently she has $8000 in cash(in youth). She can lend and borrow at the bank at 15%(i.e lending $1 in youth will give her $1.15 in old age). Her only investment opportunity other than the bank is a project that costs $5000 in her youth and has a payoff of $6000 in her old age. What is the most she can consume in her old age?
1450
To determine the most Lara Beal can consume in her old age, let's consider the different options she has:
1. Option 1: Allocating all her wealth to the bank (cash) and taking advantage of the 15% interest rate on lending.
In her youth:
- She has $8000 in cash.
- Investing in the bank will give her $8000 * 1.15 = $9200 in her old age.
In her old age:
- She can consume $9200.
2. Option 2: Investing in the project.
In her youth:
- She invests $5000 in the project.
- She has $3000 left in cash.
In her old age:
- She receives a payoff of $6000 from the project.
- She also has $3000 in cash.
- She has a total of $9000.
Comparing the outcomes of both options, Lara Beal can consume the most in her old age by choosing Option 2. Therefore, she can consume $9000.
To determine the most Lara Beal can consume in her old age, we need to compare two scenarios: investing in the project or lending the money at the bank.
1. Investing in the project:
If Lara Beal invests $5000 in the project, she will receive $6000 in her old age. Therefore, she will have a net gain of $6000 - $5000 = $1000.
2. Lending the money at the bank:
Instead of investing in the project, Lara Beal can choose to lend the money at the bank. Since she can borrow and lend at a 15% interest rate, we can calculate the future value of the initial $5000 investment in her youth:
Future value = $5000 * (1 + 0.15) = $5750
Now, let's calculate the total amount Lara Beal will have in her old age if she chooses to lend the money at the bank. She already has $8000 in cash from her youth, so:
Total amount = $8000 + $5750 = $13750
Comparing the two scenarios, we can see that Lara Beal will have the most to consume in her old age if she chooses to lend the money at the bank. Therefore, she can consume up to $13750.