Fv = pv * (1 + r)^n

Definition

The formula for future value (fv) illustrates how much an investment made today (present value, pv) will grow over time at a specified interest rate (r) for a certain number of periods (n). This concept is vital for evaluating the profitability of capital investments, as it allows decision-makers to estimate the potential returns of their investments over time. Understanding this formula helps in making informed financial decisions in capital budgeting.

5 Must Know Facts For Your Next Test

1. The formula calculates the future value based on the compounding effect of interest over multiple periods.
2. The term 'n' represents the number of time periods that the investment will earn interest, which can significantly impact the future value.
3. Higher interest rates (r) lead to greater future values, demonstrating the importance of finding favorable rates for investments.
4. This formula is foundational for capital budgeting as it helps compare the potential returns of different investment opportunities.
5. Using this formula, businesses can evaluate long-term projects by estimating how much an initial investment will be worth in the future.

Review Questions

• How does changing the interest rate (r) in the formula affect future value (fv)?
  • Changing the interest rate (r) in the formula directly influences the future value (fv). A higher interest rate increases the amount of future value, showing that investments grow faster with more favorable rates. Conversely, a lower interest rate results in a smaller future value. Therefore, it's crucial for investors to seek out higher rates to maximize their returns on investments.
• Discuss how the concept of compounding relates to capital budgeting and the use of this formula.
  • Compounding is central to understanding how investments grow over time and directly ties into capital budgeting. In capital budgeting, businesses assess long-term projects by estimating their future cash flows and determining their present values. Using the formula, companies can calculate how much an investment will be worth in the future and compare it with other projects to make informed investment decisions.
• Evaluate a scenario where an investor must choose between two projects with different time horizons and interest rates using this formula.
  • When evaluating two projects with varying time horizons and interest rates, an investor should calculate the future value for each project using the formula. For instance, if Project A offers a higher interest rate but has a shorter duration compared to Project B with a lower rate but longer duration, determining the future value allows for a clear comparison. The investor can assess which project yields a greater return over its respective timeline. This analysis aids in selecting the most financially beneficial option based on projected growth and investment potential.

Related terms

Present Value: The current worth of a future sum of money or stream of cash flows given a specified rate of return.

Interest Rate: The percentage at which money grows annually, influencing the future value of investments.

Compounding: The process in which interest is added to the principal sum, allowing earnings to generate additional earnings over time.