Lara Beal allocates wealth between two periods: youth and old age. Currently (in her youth) she has $8,000 in cash. She can lend and borrow at the bank at 15% (that is, 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 $5,000 now in her youth and has a payoff of $6,000 in her old age. What is the most she can consume in her old age?
To determine the most Lara can consume in her old age, we need to compare the return on investment from the bank and the project.
1. If Lara lends her $5,000 at the bank, it will grow to $5,000 * (1 + 15%) = $5,000 * 1.15 = $5,750 in her old age.
2. If she invests in the project, she will have $8,000 - $5,000 = $3,000 left in cash in her youth. In her old age, she will have the project's payoff of $6,000. Therefore, her total wealth in old age from the project is $3,000 + $6,000 = $9,000.
Comparing the two options, Lara should choose the project since it provides a higher return on investment. The most she can consume in her old age is $9,000.
To find out the most Lara can consume in her old age, we need to compare the return on investing in the bank to the return on investing in the project.
Investing in the bank:
Lara has $8,000 in cash at present. She can lend this amount to the bank at 15%, which means she will have $9,200 in old age ($8,000 * 1.15).
Investing in the project:
The project costs $5,000 now, but it will have a payoff of $6,000 in old age.
Comparing the returns:
If Lara invests in the bank, she will have $9,200 in old age.
If Lara invests in the project, she will have $6,000 in old age.
Considering these options, the most Lara can consume in her old age is $9,200 if she invests in the bank.
To find out the most Lara Beal can consume in her old age, we need to compare the returns from lending/borrowing at the bank and investing in the project.
Let's consider the two scenarios separately:
Scenario 1: Lending/borrowing at the bank:
- Lara Beal has $8,000 in cash in her youth.
- The bank offers a 15% interest rate.
- If she lends $1 in her youth, she will receive $1.15 in her old age.
To determine how much Lara Beal will have in her old age by lending her money at the bank, we can calculate:
Amount in old age = Amount in youth * (1 + interest rate)
Using the formula, we calculate:
Amount in old age = $8,000 * (1 + 0.15)
= $8,000 * 1.15
= $9,200
So, if Lara Beal chooses to lend her money at the bank, she will have $9,200 in her old age.
Scenario 2: Investing in the project:
- Lara Beal can invest $5,000 in a project in her youth.
- The project will yield $6,000 in her old age.
If Lara Beal chooses to invest in the project, she will receive $6,000 in her old age.
Now, we compare the outcomes from both scenarios:
- If she chooses to lend at the bank, she will have $9,200 in her old age.
- If she chooses to invest in the project, she will have $6,000 in her old age.
Therefore, the most Lara Beal can consume in her old age is $9,200 if she chooses to lend her money at the bank.