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?

Answer 1

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.