Definition
Compound Amount of One Per Period refers to the final value of a series of deposits of $1.00 per period, where each $1.00 deposit is allowed to earn interest and the interest is compounded over each period. As a result, the compound amount includes the principal deposits and the accumulated interest over the specified number of periods.
Examples
Example 1: Annual Compounding
Suppose you deposit $1.00 at the end of each year for five years into an account that pays 5% interest annually. The compound amount of one per period can be calculated as follows:
Using the future value of an annuity formula:
\[ FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right) \]
where:
- \( P = 1 \) (deposit per period)
- \( r = 0.05 \) (interest rate)
- \( n = 5 \) (number of periods)
\[ FV = 1 \times \left( \frac{(1 + 0.05)^5 - 1}{0.05} \right) \approx 5.53 \]
Therefore, the total amount is approximately $5.53 after five years.
Example 2: Quarterly Compounding
If the deposits are made quarterly, $1.00 at the end of every three months, into an account with a 4% annual interest rate, compounded quarterly for two years, the calculations vary slightly.
With an interest rate of 1% compounded quarterly, the number of periods becomes 8.
\[ FV = 1 \times \left( \frac{(1 + 0.01)^8 - 1}{0.01} \right) \approx 8.24 \]
The total amount after eight quarters is thus approximately $8.24.
Frequently Asked Questions (FAQs)
What is the ‘Compound Amount of One Per Period’ used for?
It is used in financial planning to predict the future value of a series of recurring investments or savings with compound interest.
How does the frequency of compounding affect the compound amount?
Higher frequency of compounding (e.g., monthly or quarterly) generally results in a larger compound amount compared to annual compounding due to the effects of interest-on-interest more frequently.
The formula is:
\[ FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right) \]
Can the compound amount of one per period be applied to different currencies?
Yes, the concept is universally applicable across currencies, as the principle of compounding interest remains the same.
1. Future Value (FV): The value of a current asset at a future date based on an assumed rate of growth over time.
2. Compounding Interest: The process of earning interest on both the original amount of money and any previously earned interest.
4. Interest Rate (r): The proportion of a loan or investment charged as interest to the borrower, typically expressed as an annual percentage of the loan outstanding.
Online Resources
- Investopedia - Comprehensive resource for investing, finance, and market analysis.
- Khan Academy - Offers free courses in finance and economics, including lessons on compounding interest and future value calculations.
- MoneyChimp Compound Interest Calculator - Useful for computing future values based on various compounding scenarios.
References
- “Investments” by William F. Sharpe, Gordon J. Alexander, and Jeffery V. Bailey.
- “Principles of Corporate Finance” by Richard A. Brealey, Stewart C. Myers, and Franklin Allen.
Suggested Books for Further Study
- “The Theory of Investment Value” by John Burr Williams
- “Financial Management: Theory & Practice” by Eugene F. Brigham and Michael C. Ehrhardt
- “Investment Science” by David G. Luenberger
Real Estate Basics: Compound Amount of One Per Period Fundamentals Quiz
### Is the compound amount of one per period used to calculate future value for a series of one-time or recurring investments?
- [ ] One-time investments
- [x] Recurring investments
- [ ] It can be used for both
- [ ] It cannot be used for investments
> **Explanation:** The compound amount of one per period is specifically used to calculate the future value of recurring investments, such as savings or deposits that are made regularly.
### What does each $1.00 deposit in the compound amount of one per period signify?
- [ ] A loan received monthly
- [ ] An annual expense
- [x] An investment or savings deposit per period
- [ ] A tax payment
> **Explanation:** Each $1.00 deposit represents an investment or savings deposit made per period (e.g., annually, quarterly, monthly).
### What is an essential component of the Compound Amount of One Per Period Formula?
- [ ] Population size
- [ ] Current inflation rate
- [x] Interest rate
- [ ] Government bond yields
> **Explanation:** The interest rate is a critical component because it determines the rate at which the investments grow over the period.
### How does the number of periods influence the compound amount?
- [x] More periods generally result in a larger compound amount
- [ ] It has no influence on the amount
- [ ] Fewer periods generally result in a larger compound amount
- [ ] The number of periods does not correlate to the final amount
> **Explanation:** An increase in the number of periods usually leads to a larger compound amount due to more opportunities for interest to accrue.
### What effect does higher frequency of compounding have on the compound amount?
- [ ] It reduces the compound amount
- [x] It usually increases the compound amount
- [ ] It has no effect
- [ ] Higher frequency of compounding reduces interest
> **Explanation:** Higher frequency of compounding (such as quarterly or monthly) usually increases the compound amount because interest is calculated and added more frequently.
### Does the compound amount of one per period apply equally to different interest rates?
- [ ] Yes, the interest rate doesn't matter.
- [x] No, different interest rates produce different compound amounts.
- [ ] Only higher interest rates can be used.
- [ ] It applies only to a standard interest rate of 3%.
> **Explanation:** Different interest rates will result in different compound amounts, with higher rates leading to greater amounts.
### What formula represents the compound amount of one per period?
- [ ] \\( P(1 + r)^{t-1} \\)
- [ ] \\( \dfrac{(1 + r) - 1}{r}P \\)
- [x] \\( P \times \left( \dfrac{(1 + r)^n - 1}{r} \right) \\)
- [ ] \\( P + Prt \\)
> **Explanation:** The proper formula includes the initial periodic deposit \\( P \\), the interest rate \\( r \\), and the number of periods \\( n \\).
### Are deposits in the Compound Amount of One Per Period assumed to occur at the beginning or end of each period?
- [x] End of each period
- [ ] Beginning of each period
- [ ] Either, it's flexible
- [ ] It does not specify
> **Explanation:** It is standard in these calculations to assume that deposits occur at the end of each period.
### Can the concept of compound amount be applied to alternative investments like stocks?
- [ ] No, it applies only to fixed income investments.
- [ ] It is exclusive to savings accounts.
- [x] Yes, it can be applied to any repeated investment vehicle with compounding interest.
- [ ] Only applicable to real estate investments.
> **Explanation:** The concept can universally be applied to any form of repeated investment vehicle that utilizes compounding interest principles.
### The term "compound interest" primarily indicates what?
- [x] Interest on both the initial principal and the earned interest
- [ ] Interest calculated once at the end of term
- [ ] Interest paid only on the principal
- [ ] A special high-rate interest account
> **Explanation:** Compound interest means earning interest on both the initial principal and the previously earned interest over each period.
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