Compound Amount of One
Definition
The compound amount of one is the amount that $1 would grow to if left on deposit with interest allowed to compound. Compounding interest means that the interest earned each period is added to the principal amount, and future interest calculations are based on the increased principal.
Example
Consider a dollar deposited in a bank that pays 8% interest with annual compounding. The balance each year over five years can be calculated as follows:
- Year 1: $1 * (1 + 0.08) = $1.08
- Year 2: $1.08 * (1 + 0.08) = $1.1664
- Year 3: $1.1664 * (1 + 0.08) = $1.2597
- Year 4: $1.2597 * (1 + 0.08) = $1.3605
- Year 5: $1.3605 * (1 + 0.08) = $1.4693
Therefore, if $1 is deposited at 8% annual interest, compounded yearly, it will grow to approximately $1.4693 after five years.
Frequently Asked Questions
Q1: What is the formula to calculate the compound amount?
- A: The formula to calculate the compound amount is A = P(1 + r/n)^(nt), where:
- A = the amount of money accumulated after n years, including interest.
- P = the principal amount (initial investment).
- r = annual interest rate (in decimal).
- n = number of times that interest is compounded per year.
- t = the time in years.
Q2: Why is compounding important in investments?
- A: Compounding is essential because it allows the investment to grow exponentially over time as interest itself earns interest.
Q3: What types of accounts typically offer compounded interest?
- A: Savings accounts, certificates of deposit (CDs), money market accounts, and some investment accounts offer compounded interest.
Q4: Does the frequency of compounding affect the final amount?
- A: Yes, the more frequently interest is compounded, the greater the final amount will be.
Q5: What is the difference between annual compounding and monthly compounding?
- A: With annual compounding, interest is added once per year. With monthly compounding, interest is added twelve times per year, resulting in more frequent interest accumulation and a higher final amount.
Related Terms
- Principal: The initial amount of money invested or loaned.
- Interest Rate: The percentage at which interest is charged or paid.
- Compounding: The process in which interest on a sum of money is calculated based on the initial principal and the accumulated interest from previous periods.
- Present Value: The current value of a future amount of money or stream of cash flows given a specified rate of return.
- Future Value: The value of a current asset at a future date based on an assumed rate of growth.
Online References
- Investopedia: Compound Interest
- Wikipedia: Compound Interest
- Calculation World: Compound Interest Calculator
Suggested Books for Further Studies
- “The Power of Compound Interest” by Robert Kiyosaki
- “Compound Interest: Building Wealth” by Warren Buffett
- “Investing 101” by Kathy Kristof
- “The Compound Effect” by Darren Hardy
Fundamentals of Compound Amount of One: Finance Basics Quiz
### What is the compound amount of one?
- [ ] The amount of $1 at face value.
- [ ] The amount of a currency exchange.
- [x] The amount that $1 would grow to if left on deposit with interest allowed to compound.
- [ ] A specific loan repayment scheme.
> **Explanation:** The compound amount of one refers to how much $1 will grow to if left on deposit with interest compounding over a period of time.
### What is the formula for compound interest?
- [x] A = P(1 + r/n)^(nt)
- [ ] A = P + r(n)
- [ ] A = P(1 - r/n)^(nt)
- [ ] A = P(1 + r)^(1/nt)
> **Explanation:** The correct formula for compound interest is A = P(1 + r/n)^(nt), where P is the principal, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.
### How does monthly compounding compare to annual compounding?
- [ ] It results in a lower total amount.
- [x] It results in a higher final amount.
- [ ] It has no effect on the final amount.
- [ ] It results in a lower interest rate.
> **Explanation:** Monthly compounding results in a higher final amount compared to annual compounding because interest is added more frequently.
### Over five years, which compounding frequency will yield more interest: annually or monthly?
- [ ] Annually
- [ ] Neither
- [ ] Equally
- [x] Monthly
> **Explanation:** Monthly compounding will yield more interest over five years compared to annual compounding since interest is compounded more frequently.
### Why is compounding interest important in investments?
- [ ] It limits the growth of investments.
- [ ] It has no significant impact.
- [x] It allows investments to grow exponentially.
- [ ] It provides immediate returns.
> **Explanation:** Compounding interest is important because it allows investments to grow exponentially over time as both the initial principal and the accumulated interest earn interest.
### What does the term 'Principal' refer to in compounding?
- [ ] The total interest earned.
- [x] The initial amount of money invested or loaned.
- [ ] The rate of interest.
- [ ] The period of investment.
> **Explanation:** 'Principal' refers to the initial amount of money that is invested or loaned.
### If a bank offers 5% interest compounded annually, what would be the amount after one year for a deposit of $1000?
- [ ] $1050
- [x] $1050.00
- [ ] $1005.00
- [ ] $1005
> **Explanation:** The formula A = P(1 + r/n)^(nt) makes the final amount $1050.00 after one year for a deposit of $1000 at 5% interest compounded annually.
### What factor does not affect the future value of a compounding investment?
- [ ] Principal
- [x] Currency type
- [ ] Interest rate
- [ ] Compounding frequency
> **Explanation:** The type of currency does not affect the future value of a compounding investment; principal, interest rate, and compounding frequency are the primary factors.
### How does the number of compounding periods affect the compound amount?
- [ ] It decreases the principal.
- [ ] It reduces the interest rate.
- [x] It increases the final amount.
- [ ] It has no impact.
> **Explanation:** The more frequently interest is compounded, the higher the final amount will be due to the interest-on-interest effect.
### What is present value?
- [x] The current value of a future sum of money.
- [ ] The value of money in the past.
- [ ] The final amount after interest.
- [ ] The initial investment amount.
> **Explanation:** Present value is the current value of a future sum of money or stream of cash flows given a specified rate of return.
Thank you for embarking on this journey through our comprehensive financial lexicon and tackling our challenging sample exam quiz questions. Keep striving for excellence in your financial knowledge!
