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?

Question

GPT 3.5 · Answer

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.