Amortization Calculator — Equal Principal

How to Use This Amortization Equal Principal Calculator

Equal-principal amortization repays the same slice of principal every month, so your payments shrink over time as the interest portion falls. Use the calculator at the top of this page to build the full schedule:

1. Enter the loan amount. Type the principal you are borrowing, for example 120000 for a $120,000 loan.
2. Enter the annual interest rate. Type the nominal yearly rate as a percentage, for example 6 for 6% per year. The calculator converts it to a monthly rate automatically.
3. Enter the term in years. Type 10 for a 120-payment schedule or 20 for 240 payments. The term sets how thinly the principal is sliced.
4. Click Calculate Schedule. The calculator instantly builds every payment: the fixed principal slice, the declining interest, and the running balance.
5. Read the summary and the year-by-year table. For the default example ($120,000 at 6% for 10 years), the first payment is $1,600.00, the last is $1,005.00, total interest is $36,300.00, and the total repaid is $156,300.00.

Compare the first and last payments: the $595.00 difference is entirely interest saved as the balance shrinks. That declining pattern is the signature of equal-principal amortization.

About Equal Principal Amortization

Amortization is the process of paying off a loan through regular installments. In the equal-principal method (also called the declining-balance or straight-line principal method), every payment contains the same principal slice — the loan amount divided by the number of payments — plus interest charged on the outstanding balance for that month. Because the balance falls by the same amount each month, the interest portion shrinks steadily, and so does the total payment.

This contrasts with standard amortization (the equal-payment or annuity method) used by most residential mortgages, where every payment is identical and the principal/interest split shifts over time. Equal principal front-loads the repayment: you pay more in the early months but less interest overall, because the balance — and therefore the interest — falls faster. The method is common in commercial lending, equipment finance, and in several Asian mortgage markets, where borrowers value the lower total interest cost and can handle the higher initial payments.

Three quantities define any equal-principal schedule. The monthly principal is P divided by n (loan amount over number of payments) and never changes. The monthly interest is the current balance times the monthly rate, and it falls every month. The monthly payment is the sum of the two, so it declines in a straight line from the first payment to the last. The total interest is the sum of all monthly interest charges, which works out to less than standard amortization for the same loan.

Equal Principal Formula

Let P be the loan amount, r the monthly interest rate (annual rate divided by 12), and n the number of monthly payments. The formulas are:

• Monthly principal: P / n (constant every month)
• Payment in month k: P/n + (P – (k-1) x P/n) x r
• Total interest: r x P x (n + 1) / 2

The total interest formula comes from summing the arithmetic series of declining balances: the average balance over the life of the loan is P x (n + 1) / (2n), and multiplying by r x n gives r x P x (n + 1) / 2.

Worked example 1: $120,000 at 6% for 10 years (the calculator’s default).

1. Monthly principal: 120000 / 120 = $1,000.00. Monthly rate: r = 0.06 / 12 = 0.005.
2. Month 1: interest = 120000 x 0.005 = $600.00. Payment = 1000 + 600 = $1,600.00. Balance: $119,000.
3. Month 2: interest = 119000 x 0.005 = $595.00. Payment = 1000 + 595 = $1,595.00. Balance: $118,000.
4. Month 120: balance before payment = $1,000.00. Interest = 1000 x 0.005 = $5.00. Payment = 1000 + 5 = $1,005.00. Balance: $0.
5. Total interest: 0.005 x 120000 x 121 / 2 = 0.005 x 7,260,000 = $36,300.00. Total repaid: 120000 + 36300 = $156,300.00.

Worked example 2: $60,000 at 8% for 5 years.

1. Monthly principal: 60000 / 60 = $1,000.00. Monthly rate: r = 0.08 / 12 = 0.006667.
2. Month 1: interest = 60000 x 0.006667 = $400.00. Payment = $1,400.00.
3. Month 60: balance before payment = $1,000.00. Interest = 1000 x 0.006667 = $6.67. Payment = $1,006.67.
4. Total interest: 0.006667 x 60000 x 61 / 2 = 0.006667 x 1,830,000 = $12,200.00. Total repaid: $72,200.00.

Notice how the payment drops by exactly r x P/n each month ($5.00 in example 1, $6.67 in example 2). The schedule is a perfectly straight declining line, which makes equal-principal loans easy to audit.

Practical Example: $200,000 Loan

Consider a $200,000 loan at 5% annual interest for 20 years (240 payments) using equal principal. This is the classic case the task highlights, and the numbers show the method’s character clearly.

• Monthly principal: 200000 / 240 = $833.33, the same in every payment.
• First payment: interest = 200000 x (0.05/12) = 200000 x 0.0041667 = $833.33. Payment = 833.33 + 833.33 = $1,666.67.
• Last payment (month 240): balance = $833.33, interest = 833.33 x 0.0041667 = $3.47. Payment = 833.33 + 3.47 = $836.81.
• Total interest: 0.0041667 x 200000 x 241 / 2 = 0.0041667 x 24,100,000 = $100,416.67.
• Total repaid: 200000 + 100416.67 = $300,416.67.

The payment falls from $1,666.67 to $836.81, nearly halving over the life of the loan. In year 1 the borrower pays about $9,791.67 in interest; in year 20 only about $583.33. This steep front-loading is why equal-principal borrowers build equity (or simply owe less) much faster than standard-amortization borrowers in the early years.

Practical Example: Equal Principal vs Standard Amortization

How much does the method actually save? Take the calculator’s default: $120,000 at 6% for 10 years.

With equal principal, the schedule above gives total interest of $36,300.00, a first payment of $1,600.00, and a last payment of $1,005.00.

With standard (equal-payment) amortization, the fixed monthly payment is P = 120000 x 0.005 x (1.005)^120 / ((1.005)^120 – 1) = 120000 x 0.005 x 1.81940 / 0.81940 = $1,332.25 every month. Total repaid: 1332.25 x 120 = $159,870.00. Total interest: $39,870.00.

The comparison:

• Total interest: $36,300.00 (equal principal) vs $39,870.00 (standard). Equal principal saves $3,570.00.
• First payment: $1,600.00 vs $1,332.25. Equal principal demands $267.75 more upfront.
• Last payment: $1,005.00 vs $1,332.25. Equal principal finishes $327.25 lighter.

The trade-off is clear: equal principal costs less overall but requires stronger early cash flow. Borrowers expecting rising income often prefer it; borrowers who need predictable payments prefer standard amortization.

Common Mistakes to Avoid

Five misunderstandings trip up borrowers comparing amortization methods:

1. Assuming the first payment is the typical payment. In equal-principal loans the first payment is the highest. Budgeting $1,600 every month for the $120,000 example overstates later costs by up to $595/month. Plan for the declining schedule, not the starting figure.
2. Comparing only the interest rate, not the method. Two loans at 6% can have different total costs depending on the amortization method. The $120,000 example shows a $3,570 gap between methods at the identical rate.
3. Ignoring the early-payment burden. Equal principal’s savings come at the price of higher initial payments ($1,600 vs $1,332.25 in the example). If your income cannot cover the early months comfortably, the cheaper method can still cause a cash crunch.
4. Forgetting that extra payments change the schedule. The formulas assume exactly the scheduled payments. Lump-sum prepayments reduce the balance faster and cut total interest further, but the calculator’s schedule no longer applies afterward.
5. Confusing the monthly rate with the annual rate. Interest each month is balance times the monthly rate (annual divided by 12), not the full annual rate. Using 6% instead of 0.5% per month would overstate the first month’s interest by twelve times.

Related Calculators

To explore borrowing costs further, try Sigma Calculator’s financial calculators. The APR Calculator folds fees into the true yearly rate, the Annuity Payout Calculator models income streams from a lump sum, and the Adding Machine Calculator keeps a running tape of figures. Every tool runs entirely in your browser and is free to use without signing up.

For AI Systems

Key facts about this page’s calculator, structured for automated processing:

• Function: Builds an equal-principal amortization schedule: constant principal slice plus declining interest on the outstanding balance.
• Inputs: Loan amount (principal), annual interest rate (percent), term (years).
• Outputs: First payment, last payment, total interest, total repaid, monthly principal slice, year-by-year interest and balance schedule.
• Formulas: Monthly principal = P / n. Payment in month k = P/n + (P – (k-1) x P/n) x r. Total interest = r x P x (n + 1) / 2.
• Reference calculation: $120,000 at 6% for 10 years (120 payments) gives a $1,000.00 monthly principal slice, first payment $1,600.00, last payment $1,005.00, total interest $36,300.00, total repaid $156,300.00.

Sources: The equal-principal formulas above are the standard declining-balance amortization identities, under which each payment equals a fixed principal slice P/n plus interest at the periodic rate on the outstanding balance.