Future Worth (Or Value) of One

Future Worth Future Value Compound Interest Investments Time Value of Money Finance
Future Worth, also known as the Future Value (FV), refers to the amount of money that an investment made today will grow to at a specific point in the future when interest is compounded over time.
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Definition

Future Worth (Or Value) of One, also known as the Compound Amount of One, refers to the value of an investment at a future point in time when interest has been applied. The process involves compounding, which means that interest is calculated not only on the initial principal but also on the accumulated interest from previous periods.

Formula

The Future Worth can be calculated using the following formula:

\[ FV = PV \times (1 + r)^n \]

  • FV is the future value of the investment.
  • PV is the present value (initial investment).
  • r is the interest rate per period.
  • n is the number of periods.

To find the Future Worth (FV) of one unit of currency over a specific period, you can set PV to 1 in the formula.

Examples

  1. Example 1:

    • Initial Investment (PV): $1
    • Interest Rate (r): 5% (0.05)
    • Number of Years (n): 5
    • Calculation: \[ FV = 1 \times (1 + 0.05)^5 = 1 \times 1.27628156 \approx 1.276 \]
    • Future Value: $1.28

  2. Example 2:

    • Initial Investment (PV): $1
    • Interest Rate (r): 10% (0.10)
    • Number of Years (n): 3
    • Calculation: \[ FV = 1 \times (1 + 0.10)^3 = 1 \times 1.331 \approx 1.33 \]
    • Future Value: $1.33

Frequently Asked Questions (FAQs)

1. What is the difference between Future Value and Present Value?

The Future Value (FV) indicates what a sum of money today will be worth in the future, given a certain interest rate and period of compounding. Present Value (PV) is the current value of a future sum of money, discounted at a specific interest rate.

2. What is compounding frequency, and how does it affect the Future Worth?

Compounding frequency refers to the number of times interest is applied to the principal over a period. The more frequently interest is compounded, the higher the future value will be.

3. Can Future Worth be calculated for different types of investments?

Yes, Future Worth calculations can be performed for various types of investments, including lump-sum investments, annuities, and business projects, as long as the interest rate and period are specified.

4. How can I estimate the future worth of an investment without using a formula?

Online calculators and spreadsheet software can assist in computing the future worth of an investment. Financial calculators often have built-in functions to calculate FV.

  • Present Value (PV): The current worth of a future sum of money or stream of cash flows given a specified rate of return.
  • Compound Interest: Interest calculated on the initial principal, including all previously accumulated interest.
  • Annuity: A series of equal payments at regular intervals, such as yearly, monthly, or quarterly, over a specified period.

Online References to Online Resources

  1. Investopedia - Future Value
  2. Wikipedia - Time Value of Money
  3. Khan Academy - Interest and Compound Interest

Suggested Books for Further Studies

  1. “Corporate Finance” by Stephen A. Ross, Randolph W. Westerfield, and Jeffrey Jaffe
  2. “Principles of Corporate Finance” by Richard A. Brealey, Stewart C. Myers, and Franklin Allen
  3. “Fundamentals of Financial Management” by Eugene F. Brigham and Joel F. Houston

Fundamentals of Future Worth: Finance Basics Quiz

### What does the Future Value (FV) represent in finance? - [ ] The current cash flow value. - [x] The amount an investment is worth in the future. - [ ] The initial investment amount. - [ ] None of the above. > **Explanation:** The Future Value (FV) represents the amount an investment made today will be worth in the future, taking into account interest or growth over time. ### Which formula is used to calculate the Future Worth? - [ ] PV = FV / (1 + r)^n - [x] FV = PV * (1 + r)^n - [ ] FV = PV * (1 - r)^n - [ ] PV = FV * (1 + r)^n > **Explanation:** The correct formula to calculate the Future Worth (FV) is FV = PV * (1 + r)^n, where PV is the present value, r is the interest rate, and n is the number of periods. ### If $1 is invested at an annual interest rate of 6% for 3 years, what is the Future Value? - [ ] $1.18 - [ ] $1.20 - [x] $1.19 - [ ] $1.17 > **Explanation:** FV = 1 * (1 + 0.06)^3 ≈ 1.191. The Future Value is approximately $1.19. ### What effect does increasing the number of compounding periods have on the future value? - [x] It increases the future value. - [ ] It decreases the future value. - [ ] It has no effect on the future value. - [ ] It makes the future value unpredictable. > **Explanation:** Increasing the number of compounding periods results in a higher future value because interest is being calculated more frequently on an increasing principal balance. ### How does an annual interest rate of 10% affect the future value over five years compared to an annual rate of 5%? - [ ] It would result in a lower future value. - [ ] It would cut the future value in half. - [x] It would double the future value more rapidly. - [ ] It would triple the future value instantly. > **Explanation:** A higher interest rate lets the initial amount accumulate interest faster, thus reaching a higher future value more rapidly compared to a lower interest rate. ### If the number of periods (n) is doubled while keeping the interest rate constant, what happens to the Future Value? - [x] It increases the Future Value. - [ ] It decreases the Future Value. - [ ] The Future Value remains unchanged. - [ ] The Future Value is unpredictable. > **Explanation:** Doubling the number of periods increases the Future Value because the principal has more time to earn interest. ### What term is used for interest calculated on the initial principal and also on the accumulated interest of previous periods? - [ ] Simple Interest - [ ] Effective Interest - [x] Compound Interest - [ ] Nominal Interest > **Explanation:** Compound Interest refers to interest calculated on both the initial principal and the accumulated interest from earlier periods. ### What rate is applied to find the future value in the time value of money calculations? - [x] Interest rate - [ ] Discount rate - [ ] Inflation rate - [ ] Depreciation rate > **Explanation:** The interest rate is applied in the calculation of future value to determine how much the investment will grow over time. ### In financial terms, how can the effect of compounding interest be described? - [x] Earning interest on interest - [ ] Simple addition of interest - [ ] Dividing interest annually - [ ] Ignoring interest accumulation > **Explanation:** Compounding interest means that interest is earned on both the initial principal and the accumulated interest, leading to exponential growth. ### Which financial concept does the equation FV = PV * (1 + r)^n represent? - [ ] Present Value Calculation - [ ] Loan Amortization - [x] Future Value Calculation - [ ] Depreciation Schedule > **Explanation:** The equation FV = PV * (1 + r)^n is used to calculate the Future Value of an investment given a specific present value, interest rate, and number of periods.

Thank you for diving into the intricate world of Future Worth and for engaging in our study quiz. Continue honing your understanding of financial principles!

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Wednesday, August 7, 2024
Future Worth (or Value) of One Per Period
Future Value
Amount of One Per Period January 1, 1
Annuity Factor January 1, 1
Future Value January 1, 1
Reversionary Factor January 1, 1
Terminal Value (TV) January 1, 1
Amount of One January 1, 1
Callable January 1, 1
Capital Gain Distribution January 1, 1
Capital Gains January 1, 1
Class January 1, 1

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