Which of the following is true for calculating the future value of multiple cash flows?

• A. Each cash flow must be compounded to the future date individually before summing the amounts.
• B. Only the first cash flow needs to be compounded; the rest are added at face value.
• C. The future value is calculated by discounting all cash flows to the present and then summing them.
• D. All cash flows can be simply added together without considering the time period.

Answer: (A)

Verified step by step guidance

1. Understand the concept of future value: Future value is the value of a cash flow or series of cash flows at a specific point in the future, calculated by applying compound interest over time.
2. Recognize the importance of time periods: Each cash flow occurs at a different point in time, so the time value of money must be considered. Cash flows occurring earlier or later will have different future values due to compounding.
3. Apply the formula for future value of a single cash flow: The future value of a cash flow is calculated using the formula: ${\mathrm{FV}}_n={\mathrm{PV}}_n\times \; (1\; +\; r)t$, where ${\mathrm{PV}}_n$ is the present value of the cash flow, $r$ is the interest rate, and $t$ is the time period until the future date.
4. Compound each cash flow individually: Since each cash flow occurs at a different time, calculate the future value of each cash flow separately using the formula above. This ensures that the time value of money is accurately accounted for.
5. Sum the future values: After calculating the future value of each individual cash flow, add them together to determine the total future value of all cash flows.