Benton's income in period 1 (current) is $50,000. His income in period 2 (future) will be $60,000. The interest rate is 10%. At that interest rate, Benton chooses to consume $75,000 in period 1.

a. How much will Benton be able to consume in period 2?

b. If the interest rate increases to 12%, is Benton better off, worse off, or indifferent? (Trick question - all are possible.) Explain your answer using diagrams.

Benton's consumption in period 1 is $75,000, which exceeds his current income of $50,000. To finance this excess consumption, Benton borrows at an interest rate of 10%. In period 2, his income increases to $60,000, and he needs to repay the principal and interest on the loan. To determine the amount Benton can consume in period 2, we need to calculate the future value of the loan.

Using the formula for future value of a single sum with compound interest: FV = PV × (1 + r)^n, where FV is the future value, PV is the present value, r is the interest rate, and n is the number of periods.

In this case, the present value (PV) is $75,000, the interest rate (r) is 10% or 0.1, and the number of periods (n) is 2. Plugging these values into the formula, we get:

FV = $75,000 × (1 + 0.1)^2 = $75,000 × 1.1^2 = $75,000 × 1.21 = $90,750

Therefore, Benton will be able to consume $90,750 in period 2. However, since his income in period 2 is only $60,000, he won't be able to repay the full loan amount and will face a shortfall. Thus, he will only be able to consume the amount of his income, which is $60,000.

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