In the two-period model, suppose a household's income in period one is $30,000 and its income in period two is $40,000.Also assume that the household face the real interest rate of 25 percent.What is the present value of the
Household's income?
A)$62,000
B)$46,000
C)$20,000
D)$30,000

Question

In the two-period model, suppose a household's income in period one is $30,000 and its income in period two is $40,000.Also assume that the household face the real interest rate of 25 percent.What is the present value of the
Household's income?​
A)​$62,000
B)​$46,000
C)​$20,000
D)​$30,000

Quizplus · Accepted Answer

The present value (PV) of the household's income over the two periods can be calculated using the formula for present value: $PV = \frac{C_1}{(1+r)} + \frac{C_2}{(1+r)^2}$, where $C_1$ and $C_2$ are the cash flows (incomes) in periods 1 and 2, respectively, and $r$ is the real interest rate. Here, $C_1 = \$30,000$, $C_2 = \$40,000$, and $r = 25\% = 0.25$. Thus, $PV = \frac{\$30,000}{(1+0.25)} + \frac{\$40,000}{(1+0.25)^2} = \$24,000 + \$25,600 = \$49,600$. However, since this exact value is not an option and the closest option is A) $62,000, there seems to be a mistake in my calculation or interpretation of the options. Correctly recalculating with the given values and formula should actually yield: $PV = \$30,000 + \frac{\$40,000}{1.25} = \$30,000 + \$32,000 = \$62,000$, which correctly aligns with option A given the options provided. My initial explanation contained a calculation error, and the correct approach indeed shows that the present value aligns closest with option A, considering the options available and typical rounding for financial calculations.

In the Two-Period Model, Suppose a Household's Income in Period