Enter the loan information
The scheduled payment is based on principal, interest rate, term, and payment frequency. An optional extra-principal payment can be limited to a specific start and end date.
Loan Terms
Enter the amount borrowed, annual rate, term, and payment frequency.
Optional Extra Principal
Apply the extra amount only to payments dated within the selected range.
Enter 0 for no extra principal. When the amount is greater than 0, both extra-principal dates are required and are inclusive.
Formula
Payment = P × [r(1 + r)n] ÷ [(1 + r)n − 1]
P is the principal, r is the periodic interest rate, and n is the total number of scheduled payments. Extra principal does not change the scheduled payment; it reduces the balance during the selected date range.
LutherMaddy Learning Framework
Understand, Practice, and Teach
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Concept Guide
Understanding Loan Payments and Amortization
A loan amortization schedule shows how each payment is divided among interest, scheduled principal, optional extra principal, and the remaining balance.
How is the payment determined?
The scheduled payment depends on the amount borrowed, periodic interest rate, and number of payments. The payment is designed to reduce the balance to zero by the end of the term.
How does amortization work?
Interest is calculated from the outstanding balance. The rest of the scheduled payment reduces principal, so later payments generally contain less interest and more principal.
How does the extra-principal date range work?
The selected extra amount is applied only to payment dates from the chosen start date through the chosen end date. It appears separately in the schedule and directly reduces the balance.
Common mistakes
- Entering the annual rate as a decimal when the field expects a percentage.
- Using inconsistent time periods for the rate and number of payments.
- Assuming extra principal changes the scheduled payment amount.
- Selecting an extra-principal end date before the start date.
- Comparing total payments without also comparing payoff time and total interest.
Continue learning
Chapter : Excel Loan Amortization Lesson
Learn how to build the payment formula and complete amortization schedule in Microsoft Excel.
Practice
Generate a realistic problem, solve it, and check your answer.
Companion lesson
Return to the written chapter
Review the explanation, examples, videos, and guided practice in the related lesson.
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Loan Payment and Amortization Calculator: Instructor Resources
Instructor Resources
A classroom-ready guide that can be edited in this calculator's configuration file.
Learning objectives
- Calculate a periodic installment-loan payment.
- Explain the interest and principal portions of a payment.
- Construct and interpret an amortization schedule.
- Evaluate the effect of extra principal during a selected period.
Prerequisite knowledge
- Percent and decimal conversions
- Exponents
- Basic loan terminology
- Reading a financial table
Teaching outline
- Identify principal, annual rate, term, and payment frequency.
- Convert the annual rate to a periodic rate.
- Calculate the scheduled payment.
- Build the amortization schedule row by row.
- Add a date-limited extra-principal strategy and compare outcomes.
Key concepts
- Interest is based on the current balance.
- Scheduled principal equals scheduled payment minus interest.
- Extra principal is separate from scheduled principal.
- Earlier extra principal generally saves more interest than later extra principal.
Classroom demonstration
- Calculate a loan with no extra principal, then apply the same extra amount for only the first year and compare payoff time and interest.
Questions to ask
- Why is extra principal more powerful earlier in the loan?
- Why does the scheduled payment remain unchanged when extra principal is added?
- How might a borrower choose a realistic extra-payment period?
Teaching notes
- Distinguish the scheduled payment from the actual payment when extra principal is active.
- Use the separate extra-principal column to prevent students from confusing the two principal amounts.
- Connect the calculator to the Excel lesson for students who need to understand the formulas.
Assessment ideas
- Have students calculate a payment and identify the first payment’s interest and principal.
- Compare two extra-principal date ranges using the same loan.
- Ask students to explain why total interest changes.
Grading rubric
| Criterion | Points |
|---|---|
| Correct scheduled payment | 3 |
| Correct schedule components | 2 |
| Correct extra-principal date range | 2 |
| Accurate payoff and interest comparison | 2 |
| Interpretation | 1 |
| Total | 10 |
Exam and discussion questions
Basic
- Calculate the monthly payment for a stated principal, annual rate, and term.
Applied
- Compare the payoff time and total interest with and without extra principal for a specified period.
Conceptual
- Explain why extra principal reduces future interest.
Lesson instructor guide
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Open the lesson-specific guide for the full chapter teaching flow.