Amount of One Per Period

Finance Annuities Compound Interest Future Value Investments
The amount of one per period refers to the compound amount that accumulates when one unit of currency is invested at the end of each period for a certain number of periods at a specific interest rate. This concept is critical in understanding the future value of annuities in finance.
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Definition

The amount of one per period (also known as the compound amount of one per period) is a financial concept that determines the future value of an annuity when a series of equal payments (or deposits) are made at the end of each period over a specific number of periods, given a particular interest rate. This calculation is crucial in various financial operations, including savings plans, pension funds, and loan repayments.

Examples

  1. Savings Plan Example:
    • If you invest $1,000 at the end of each year into a savings account with an annual interest rate of 5% for 5 years, the future value of these investments will be calculated using the amount of one per period formula.
  2. Pension Fund:
    • A pension fund receiving equal annual contributions will use this concept to calculate the fund’s value at retirement.
  3. Loan Repayment:
    • For loans involving regular payments, understanding the future value based on these payments helps in determining total interest paid over the loan’s life.
Year Payment ($) Interest Rate (%) Periods (n) Future Value ($)
1 1000 5 5 5525.63

Frequently Asked Questions

  1. What is the formula for the amount of one per period?

    • The formula is: \( FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right) \), where \(P\) is the periodic payment, \(r\) is the interest rate per period, and \(n\) is the total number of periods.

  2. How is this concept used in finance?

    • It is primarily used to calculate the future value of regular investments or savings, and to determine the financial outcome of annuities.

  3. Can this be applied to different compounding frequencies?

    • Yes, the formula can be adapted for different compounding frequencies (monthly, quarterly, etc.) by adjusting the interest rate and number of periods accordingly.

  4. What is the difference between the amount of one per period and the future value of a lump sum?

    • The amount of one per period deals with a series of equal payments over time, whereas the future value of a lump sum deals with a single investment amount compounded over time.

  5. Is the amount of one per period applicable to both investments and loans?

    • Yes, it applies to both scenarios where regular payments or investments are made.
  • Annuity: A series of equal payments made at regular intervals.
  • Compound Interest: Interest on interest - the effect of earning interest on both the initial principal and the accumulated interest from previous periods.
  • Future Value (FV): The value of an investment at a specific date in the future.
  • Present Value (PV): The current value of a future sum of money or stream of cash flows given a specified rate of return.

Online References

Suggested Books for Further Studies

  1. “Principles of Corporate Finance” by Richard A. Brealey, Stewart C. Myers, and Franklin Allen
  2. “Fundamentals of Financial Management” by Eugene F. Brigham and Joel F. Houston
  3. “Financial Management: Theory & Practice” by Eugene F. Brigham and Michael C. Ehrhardt
  4. “Investments” by Zvi Bodie, Alex Kane, and Alan J. Marcus

Fundamentals of Amount of One Per Period: Finance Basics Quiz

### What is the primary use of the amount of one per period? - [x] To calculate the future value of annuities with regular payments. - [ ] To determine the present value of a single payment. - [ ] To establish an account's current balance. - [ ] To calculate depreciation for buildings. > **Explanation:** The amount of one per period is used to find the future value of annuities, where regular payments are made at the end of each period. ### What variables are needed to calculate the amount of one per period? - [x] Periodic payment amount, interest rate, number of periods. - [ ] Discount rate, future value, number of payments. - [ ] Present value, rate of return, inflation rate. - [ ] Annual revenue, investment growth, risk premium. > **Explanation:** The essential variables are the periodic payment amount, interest rate, and the total number of periods. ### Which formula correctly represents the amount of one per period? - [ ] \\( PV = \frac{FV}{(1 + r)^n} \\) - [ ] \\( A = P(1 + rt) \\) - [x] \\( FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right) \\) - [ ] \\( I = PRT \\) > **Explanation:** \\( FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right) \\) is the correct formula for calculating the future value of an annuity with regular payments. ### What does 'r' represent in the formula \\( FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right) \\)? - [ ] Future value. - [x] Interest rate per period. - [ ] Discount factor. - [ ] Number of payments. > **Explanation:** In this formula, 'r' stands for the interest rate per period. ### If $1,000 is invested annually at an interest rate of 5% for 5 years, which value represents 'n'? - [x] 5 - [ ] 1000 - [ ] 0.05 - [ ] 5000 > **Explanation:** 'n' represents the number of periods, which in this instance is 5 years. ### What happens to the future value if the interest rate increases, assuming all other factors remain constant? - [ ] It decreases. - [x] It increases. - [ ] It remains the same. - [ ] It first increases then decreases. > **Explanation:** An increase in the interest rate typically results in a higher future value for the series of payments. ### Is the amount of one per period relevant for both investments and loans? - [x] Yes - [ ] No - [ ] Only for investments - [ ] Only for loans > **Explanation:** This concept is relevant to both scenarios where regular payments or investments are made. ### Which type of compounding does the formula \\( FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right) \\) assume? - [ ] Continuous compounding - [x] Discrete compounding - [ ] Daily compounding - [ ] Quarterly compounding > **Explanation:** The formula is based on discrete compounding principles, where interest is compounded at regular intervals. ### What is the outcome called when calculating \\( FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right) \\)? - [ ] Present Value - [ ] Rate of Return - [x] Future Value - [ ] Internal Rate of Return (IRR) > **Explanation:** The outcome of this equation is referred to as the future value. ### What distinguishes an annuity from a single lump-sum investment in future value calculations? - [x] Regular periodic payments - [ ] Initial investment size - [ ] The interest rate used - [ ] Inflation effects > **Explanation:** Annuities are characterized by regular periodic payments, whereas lump-sum investments involve a single payment.

Thank you for exploring the important financial concept of the amount of one per period, delving into its practical applications, and testing your knowledge with our quiz. Continue building your financial acumen!

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Wednesday, August 7, 2024
Ampersand (&)
Amount of One
Future Worth (Or Value) of One January 1, 1
Fixed-Income January 1, 1
Perpetuity January 1, 1
Terminal Value (TV) January 1, 1
Amount of One January 1, 1
Annuity Factor 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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