Installment to Amortize One Dollar
Installment to Amortize One Dollar is a mathematically computed factor derived based on compound interest functions. This factor illustrates the amount required as a periodic payment to fully repay a $1.00 loan over a specified period of time. For the installment amount to meet its objective, it must exceed the periodic interest rate applicable to the loan.
Examples
To provide a clearer understanding, here are a few examples that illustrate different scenarios for amortizing one dollar:
- $0.2638 is needed to amortize $1.00 at 10% interest over 5 yearly payments.
- $0.1627 is needed to amortize $1.00 at 10% interest over 10 yearly payments.
- $0.1175 is needed to amortize $1.00 at 10% interest over 20 yearly payments.
Frequently Asked Questions (FAQs)
Q: How is the installment to amortize one dollar calculated?
A: This calculation involves using the annuity formula for computing the periodic payment required to repay a loan with compound interest. The formula generally involves the interest rate, number of periods, and the present value of the loan.
Q: Why must the periodic installment exceed the periodic interest rate?
A: The periodic installment exceeding the periodic interest rate ensures that the loan principal is gradually reduced each payment period, eventually retiring the entire loan after the specified number of periods.
Q: Is this concept applicable to both personal and commercial loans?
A: Yes, the concept can be understood and applied to both personal and commercial loans for calculating periodic payments required for amortization.
Q: Can this concept be used for different interest rates and periods?
A: Yes, different interest rates and periods can be accommodated by recalculating the installment to amortize one dollar using the appropriate formula.
Q: Where can I find tools to calculate these values easily?
A: Numerous online calculators and financial software packages can compute amortization schedules and required payments based on input values of interest rate, whether the loan is composite or simple, period length, and more.
- Amortization: The process of gradually reducing a loan through periodic payments covering both principal and interest until the loan is repaid in full.
- Amortization Schedule: A table detailing each periodic payment on a loan over time, showing the amount applied to interest, the amount applied to principal, and the remaining balance.
- Compound Interest: Interest calculated on the initial principal and also on the accumulated interest of previous periods.
- Periodic Payment: A regular payment made in intervals, such as monthly or annually, to repay an installment loan.
Online Resources
References
- Fabozzi, F.J., & Franco, M.G. (2007). Fixed Income Securities: Tools for Today’s Markets (3rd ed.). Wiley.
- Bodie, Z., Kane, A., & Marcus, A.J. (2017). Investments (11th ed.). McGraw-Hill Education.
- Brigham, E.F., & Ehrhardt, M.C. (2019). Financial Management: Theory & Practice (16th ed.). Cengage Learning.
Suggested Books for Further Studies
- “Theory of Interest” by Stephen G. Kellison
- “Principles of Corporate Finance” by Richard A. Brealey, Stewart C. Myers, and Franklin Allen
- “Financial Modeling” by Simon Benninga
- “Real Estate Finance and Investments” by William Brueggeman and Jeffrey Fisher
Real Estate Basics: Installment to Amortize One Dollar Fundamentals Quiz
### What does the term "Installment to Amortize One Dollar" primarily represent?
- [ ] The interest rate on a loan.
- [x] The periodic payment required to fully repay a $1.00 loan over a specified period.
- [ ] The total loan amount.
- [ ] A preferred loan term.
> **Explanation:** The term represents the periodic payment necessary to amortize (pay off) a $1.00 loan over a specific period.
### Can the Installment to Amortize One Dollar be applied to both personal and commercial loans?
- [x] Yes, it can apply to both.
- [ ] No, it only applies to personal loans.
- [ ] No, it only applies to commercial loans.
- [ ] It depends on the interest rate.
> **Explanation:** This concept applies to both personal and commercial loans, assuming appropriate calculation based on respective terms.
### How does the length of the loan repayment period affect the installment amount required to amortize one dollar?
- [ ] It does not affect the installment amount.
- [x] The longer the repayment period, the lower the installment amount.
- [ ] The installment amount is higher for longer periods.
- [ ] It lowers the interest rate.
> **Explanation:** The longer the period over which the loan is repaid, the lower the required installment amount due to the extended amortization period.
### What happens if the periodic installment amount is less than the periodic interest rate?
- [x] The loan balance may increase.
- [ ] The loan will be paid off faster.
- [ ] It has no effect on the loan balance.
- [ ] The loan interest rate will go down.
> **Explanation:** If the installment amount is lower than the periodic interest, it can lead to negative amortization, making the loan balance increase because the payments don't cover the interest due.
### What is the impact of a higher interest rate on the required installment to amortize one dollar?
- [x] Higher interest rates increase the required installment.
- [ ] It lowers the necessary installment.
- [ ] There’s no impact on installment amount.
- [ ] It shortens the loan term.
> **Explanation:** A higher interest rate increases the amount of each periodic installment needed to fully repay the loan due to higher interest costs.
### At a 10% yearly interest rate, what is the installment required to amortize one dollar over 10 years?
- [x] $0.1627
- [ ] $0.2638
- [ ] $0.1175
- [ ] $0.1000
> **Explanation:** The periodic installment necessary at a 10% interest rate over 10 years is $0.1627.
### Does the term "Compound Interest" relate to Installment to Amortize One Dollar?
- [x] Yes, it is based on compound interest functions.
- [ ] No, it is unrelated.
- [ ] It only relates to simple interest.
- [ ] It impacts the term's duration only.
> **Explanation:** The installment to amortize one dollar is derived from compound interest formulas used to calculate the requisite payments over time.
### What constitutes an effective amortization schedule for loan repayments?
- [ ] Random calculations.
- [ ] Only the interest portion is needed.
- [ ] Complete details per period for interest, principal, and remaining balance.
- [x] A detailed table showing interest, principal, and remaining balance per period.
> **Explanation:** An amortization schedule should provide detailed breakdowns of each periodic payment, showing the part going towards interest, principal, and the remaining loan balance.
### What does the term “Periodic Payment” refer to in loan amortization?
- [x] Regularly scheduled installments to repay a loan.
- [ ] Lump sum payments only.
- [ ] Payments made randomly or without schedule.
- [ ] Any non-scheduled financial transaction.
> **Explanation:** Periodic payments are regular installments made according to a predefined schedule to amortize a loan.
### What can generate an amortization schedule for a given loan easily?
- [x] Online amortization calculators.
- [ ] Manual arithmetic only.
- [ ] Random estimations.
- [ ] Projections without interest calculation.
> **Explanation:** Online amortization calculators can be used to easily generate accurate amortization schedules for loans.
