When you borrow money, you have to repay the amount of money you borrowed plus the interest the loan accumulates over the term of the loan. You repay the loan by making regular payments over the term of the loan. Each payment does two things: it pays all of the interest due on the loan at the time the payment is made and the remainder of the payment goes to paying down the loan amount. This process of gradually repaying the loan with periodic payments over the term of the loan is called
amortization.
Amortization is a process by which the principal of a loan is extinguished over the course of an agreed-upon time period through a series of regular payments that go toward both the accruing interest and principal reduction. (the process of spreading out a loan or asset cost into
equal payments over time. Each payment typically includes both
interest and
principal.) Two components make up the agreed-upon time component.
- Amortization Term. The amortization term is the length of time for which the interest rate and payment agreement between the borrower and the lender will remain unchanged. Thus, if the agreement is for monthly payments at a 5% fixed rate over five years, it is binding for the entire five years. Or if the agreement is for quarterly payments at a variable rate of prime plus 2% for three years, then interest is calculated on this basis throughout the three years.
- Amortization Period. The amortization period is the length of time it will take for the principal to be reduced to zero. For example, if you agree to pay back your car loan over six years, then after six years you reduce your principal to zero and your amortization period is six years.
In most relatively small purchases, the amortization term and amortization period are identical. For example, a vehicle loan has an agreed-upon interest rate and payments for a fixed term. At the end of the term, the loan is fully repaid. However, sometimes with larger purchases such as real estate transactions, financial institutions hesitate to agree to amortization terms of much more than five to seven years because of the volatility and fluctuations of interest rates. As a result, a term of five years may be established with an amortization period of 25 years. When the five years elapse, a new term is established as agreed upon between the borrower and lender. The conditions of the new term reflect prevailing interest rates and a payment plan that continues to extinguish the debt within the original amortization period.
Amortization Schedules
An amortization schedule shows the payment amount, principal component, interest component, and remaining balance for every payment in the annuity. As the title suggests, it provides a complete understanding of where the money goes, identifying how much of each payment goes to interest and how much goes to principal
An amortization schedule has five columns:
- Payment Number. There is a row for every payment made to repay the loan.
- Payment. The periodic payment made to repay the loan. All of the payments are the same (PMT), except for the last payment.
- Interest Paid. For each row, the interest paid entry is the amount of interest due on the loan at the time of the corresponding payment.
- Principal Paid. For each row, the principal paid entry is the amount of principal repaid at the time of the corresponding payment, after the interest is paid.
- Balance. For each row, the balance records how much of the original loan amount remains after the payment is made.
To fill in an amortization schedule, you first need to have all of the details about the loan, including the loan amount (PV), the payment (PMT), the number of payments (N), and the interest rate. If any of these quantities are missing, calculate out the missing value before completing the amortization schedule.
| Payment Number | Payment | Interest Paid (INT) | Principal Paid (PRN) | Balance (BAL) |
| 0 | | | | Loan Amount1 |
| 1 | PMT2 | INT3 | PRN4 | BAL5 |
| 2 | PMT2 | INT3 | PRN4 | BAL5 |
| | | | |
| N-1 | PMT2 | | | |
| N | Final Payment10 | Final INT9 | Final PRN8 | 07 |
| Totals | Total Amount Paid12 | Total Interest Paid13 | Total Principal Paid11 | |
Follow these steps to fill in the amortization schedule.
1. In row 0, the only entry is the loan amount in the balance column.
2. Fill in the rounded loan payment down the payment column, except for the last payment.
3. Calculate the interest paid portion of the payment. The interest is the balance from the previous row times the periodic interest rate:
Interest Paid = Balance from Previous Row x i.Note: this calculation assumes that the payment frequency and the compound frequency for the interest rate are the same (i.e. a simple annuity).
4. Calculate the principal paid portion of the payment. The principal paid is the difference between the payment and the interest paid:
Principal Paid = PMT - Interest Paid.
5. Calculate the outstanding balance on the loan after the payment is made. The balance is difference between the balance in the previous row and the principal paid:
Balance = Balance from Previous Row - Principal Paid.
6. For each payment, repeat steps 2 through 5, except for the last row.
7. The last balance entry is 0. Because this is the last payment, the loan must be paid off, which means the balance is reduced to 0.
8. The final principal paid entry equals the balance entry from row N-1.
9. Calculate the final interest paid portion in the same way as in step 3.
10. The final payment is the sum of the final interest paid entry and the final principal paid entry:
Final Payment = Final INT + Final PRIN.
11. The total principal paid is the sum of the principal paid column, and is just the loan amount:
Total Principal Paid = Loan Amount.
12. The total amount paid is the sum of the payment column:
Total Amount Paid = (N-1) x PMT + Final Payment
13. The total interest paid is the sum of the interest paid column, and equals the difference between the other two column totals: Total Interest Paid = Total Amount Paid - Total Principal Paid.
Note: The manual calculation of the interest paid entry above is based on the assumption that the payment frequency and the compounding frequency are equal. If the payment frequency and the compounding frequency are not equal, an interest conversion is required to convert the interest rate to the equivalent rate with the compounding frequency equal to the payment frequency. However, if you use the TI BAII Plus’s built-in amortization worksheet (described below), no interest conversion is required.
Example:
A $3,000 loan at 8% compounded quarterly is repaid with quarterly payments of $800. Construct the amortization schedule for the loan.
Because the payment frequency and the compounding frequency are equal, no interest conversion is required. The calculations for each entry are shown in blue. The periodic interest rate is i = 8%/4 = 2%
