refer to the two cash - flow diagrams. f1 and f2 are the corresponding future worth values of the four…

refer to the two cash - flow diagrams. f1 and f2 are the corresponding future worth values of the four uniform periodic cash flows a based on the given variable periodic interest rates. what is the relationship between f1 and f2? a. f1 = f2 b. f1 < f2 c. not enough information to determine d. f1 > f2

refer to the two cash - flow diagrams. f1 and f2 are the corresponding future worth values of the four uniform periodic cash flows a based on the given variable periodic interest rates. what is the relationship between f1 and f2? a. f1 = f2 b. f1 < f2 c. not enough information to determine d. f1 > f2

Answer

Explanation:

Step1: Recall future - worth formula for non - uniform interest rates

The future worth $F$ of a series of equal cash flows $A$ with different interest rates $i_n$ over $n$ periods is calculated using the compound - interest formula $F = A\sum_{n = 1}^{N}(1 + i_n)$.

Step2: Analyze the cash - flow diagrams

In the first cash - flow diagram for $F1$, the interest rates are $4%$, $5%$, and $6%$ from period 1 to 3 respectively. In the second cash - flow diagram for $F2$, the interest rates are $6%$, $5%$, and $4%$ from period 1 to 3 respectively. Let the cash flow in each period be $A$. For $F1$, $F1=A(1 + 0.04)(1 + 0.05)(1 + 0.06)=A\times1.04\times1.05\times1.06 = A\times1.15752$. For $F2$, $F2=A(1 + 0.06)(1 + 0.05)(1 + 0.04)=A\times1.06\times1.05\times1.04 = A\times1.15752$.

Answer:

A. F1 = F2