Lara allocates wealth between two periods: youth (time 1) and old age (time 2). Currently (in her youth) she has $8,000 in cash. She can borrow and lend at the bankat a rate of 15% between time 1 and time 2 (that is, lending $1 in youth will give her$1.15 in old age). Her only investment opportunity other than the bank is a projectthat costs $5,000 now in her youth and has a payoff of $6,000 in her old age. What isthe most Lara can consume in her old age? Assume Lara cannot consume a negativeamount in her youth.

The second alternative is the one that will allow her to consume more in her old age.

Explanation:

Giving the following information:

Lara allocates wealth between two periods: youth (time 1) and old age (time 2).

In her youth, she has $8,000 in cash. She can borrow and lend at the bank at a rate of 15% between time 1 and time 2.

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.

Alternative A:

We will use the final value formula.

FV = Present Value * (1+i) ^n

FV = 8000 * (1.15) ^1 = $9200

Alternative B:

Receive $6000

Invest 3000 = 3000 * (1.15) ^1 = 3450

Total = $9450

The second alternative is the one that will allow her to consume more in her old age.