Amount of One

Definition

The Amount of One, or Compound Amount of One, is the future value of a single unit of currency, such as one dollar, after it has been invested at a given interest rate for a certain number of compounding periods. This concept is essential for understanding the time value of money, which asserts that a sum of money in the present is worth more than that same sum in the future due to its earning potential.

Formula

The formula to calculate the Compound Amount of One is: $ FV = PV \times (1 + r)^n $

Where:

$ FV $ = Future Value
$ PV $ = Present Value (often set to 1 for this metric)
$ r $ = Interest rate per period
$ n $ = Number of compounding periods

Examples

Example 1: If you invest $1 at an annual interest rate of 5% compounded annually for 3 years, the future value would be: $ FV = 1 \times (1 + 0.05)^3 = 1.1576 $.
Example 2: If you invest $1 at an annual interest rate of 3% compounded semi-annually (twice a year) for 4 years, the future value would be: $ FV = 1 \times (1 + 0.03/2)^{4 \times 2} = 1.12749 $.

Frequently Asked Questions (FAQs)

What is the significance of the compound amount of one?
- The compound amount of one helps investors understand how their investments will grow over time due to the compounding effect.
How does the compounding frequency affect the compound amount of one?
- The more frequently interest is compounded, the higher the future value will be, because interest is being calculated and added to the principal more often.
Can I use the compound amount of one to compare different investments?
- Yes, it helps compare the growth potential of different investment opportunities with different interest rates and compounding periods.
Is the compound amount of one applicable to all types of investments?
- It is mainly used for fixed-interest financial products such as savings accounts, certificates of deposits, and bonds.

Present Value (PV): The current value of a future sum of money, discounted at an appropriate rate of interest.
Future Value (FV): The value of a current asset at a specified date in the future, based on an assumed rate of growth.
Compounding: The process of generating earnings on an asset’s reinvested earnings.
Interest Rate: The percentage at which interest is charged or paid.

Online References

Suggested Books

Principles of Corporate Finance by Richard A. Brealey, Stewart C. Myers, and Franklin Allen.
Fundamentals of Financial Management by Eugene F. Brigham and Joel F. Houston.
Corporate Finance: The Core by Jonathan Berk and Peter DeMarzo.

Fundamentals of Amount of One: Finance Basics Quiz

### What does the term 'Compound Amount of One' signify in finance? - [ ] The present value of an investment. - [x] The future value of $1 invested at a given rate for a specified period. - [ ] The interest accrued on an investment per period. - [ ] The monthly payment on a loan. > **Explanation:** The Compound Amount of One refers to the future value of a single unit of currency invested at a specified interest rate over a certain number of periods. ### When is an amount of $1 at a 6% annual interest rate compounded yearly for 2 years? - [ ] $1.24 - [ ] $1.06 - [x] $1.1236 - [ ] $1.12 > **Explanation:** Using the formula \$ FV = 1 \times (1 + 0.06)^2 = 1.1236 \$. ### Which of the following formulas calculates the compound amount of one? - [ ] \$ FV = PV \times \frac{1}{(1 + r)^n} \$ - [ ] \$ FV = PV + (r \times n) \$ - [x] \$ FV = PV \times (1 + r)^n \$ - [ ] \$ (1 + r)^n = PV \times FV \$ > **Explanation:** The correct formula for the compound amount of one is \$ FV = PV \times (1 + r)^n \$. ### If the interest is compounded semi-annually, what would be the period rate for an annual interest rate of 8%? - [ ] 8% - [x] 4% - [ ] 2% - [ ] 16% > **Explanation:** If interest is compounded semi-annually, the period rate is half of the annual rate, which is 4% in this case. ### How does an increased compounding frequency affect the compound amount of one? - [ ] It decreases the future value. - [ ] It has no effect. - [x] It increases the future value. - [ ] It reduces the interest rate. > **Explanation:** An increased compounding frequency increases the future value because interest is being calculated and reinvested more frequently. ### An investment of $1 at 10% annual interest compounded quarterly for 1 year will yield what amount? - [ ] $1.10 - [ ] $1.25 - [ ] $1.121 - [x] $1.1038 > **Explanation:** Using the formula for quarterly compounding: \$ FV = 1 \times (1 + 0.10/4)^{4 \times 1} = 1.1038 \$. ### Over which period does compounding yield the greatest amount of interest? - [x] Quarterly - [ ] Semi-annually - [ ] Annually - [ ] Monthly > **Explanation:** The more frequent the compounding, the greater the yield, hence quarterly compounding maximizes the interest. ### What would the future value be for a $1 investment at 5% annual interest compounded biannually over 2 years? - [ ] $1.1025 - [x] $1.1038 - [ ] $1.0525 - [ ] $1.2625 > **Explanation:** Using biannual compounding: \$ FV = 1 \times (1 + 0.05/2)^{2 * 2} = 1.1038 \$. ### Why do investment analysts rely on the compound amount of one? - [ ] To calculate upfront costs. - [x] To predict the growth potential of investments over time. - [ ] To assess market conditions. - [ ] To establish risk factors. > **Explanation:** The compound amount of one helps analysts predict the future value and growth potential of investments. ### What compounding frequency results in the highest future value with the same interest rate? - [x] Daily - [ ] Monthly - [ ] Quarterly - [ ] Annual > **Explanation:** The more frequently interest is compounded, the higher the future value, with daily compounding yielding the highest future value.

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