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
- Savings Plan Example:
- If you invest $1,000 at the end of each year into a savings account with an annual interest rate of 5% for 5 years, the future value of these investments will be calculated using the amount of one per period formula.
- Pension Fund:
- A pension fund receiving equal annual contributions will use this concept to calculate the fund’s value at retirement.
- Loan Repayment:
- For loans involving regular payments, understanding the future value based on these payments helps in determining total interest paid over the loan’s life.
| Year | Payment ($) | Interest Rate (%) | Periods (n) | Future Value ($) |
|---|---|---|---|---|
| 1 | 1000 | 5 | 5 | 5525.63 |
Frequently Asked Questions
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.
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.
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.
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.
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.
Related Terms
- 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
- “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
- “Financial Management: Theory & Practice” by Eugene F. Brigham and Michael C. Ehrhardt
- “Investments” by Zvi Bodie, Alex Kane, and Alan J. Marcus
Fundamentals of Amount of One Per Period: Finance Basics Quiz
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