Hong Life CalculatorsUnderstanding the equal principal repayment calculator — concept and principle
With equal principal repayment (also called constant amortization), you repay the same amount of principal every month and pay interest on the remaining balance. The first payment is the largest and payments shrink steadily to the end. This calculator shows the first and last payment, the fixed principal portion, total interest, and how much interest you save compared with an equal-payment (annuity) loan of the same rate and term.
How it is calculated
With loan P, monthly rate i = annual rate ÷ 12 and N = years × 12:
- Principal each month = P ÷ N.
- Interest in month k = remaining balance × i, where the balance before month k is P − (P ÷ N)(k − 1).
- First payment = P ÷ N + P × i; last payment = (P ÷ N)(1 + i).
- Total interest = i × P × (N + 1) ÷ 2.
- Annuity comparison: A = P × i ÷ (1 − (1 + i)^−N), interest = A × N − P.
The principle
Interest is always charged on what you still owe. Because the balance falls by the same amount every month, it declines in a straight line, and so does the interest. The average balance over the loan is about half the original amount, which gives the (N + 1) ÷ 2 factor. An annuity loan keeps the payment flat by repaying less principal at the start, so its balance stays higher for longer and more interest accrues in total.
Worked example
Default inputs: $200,000, 6% a year, 30 years (360 months).
- Principal each month: 200,000 ÷ 360 = $555.56; monthly rate 0.5%.
- First payment: 555.56 + 200,000 × 0.005 = $1,555.56.
- Last payment: 555.56 × 1.005 = $558.33.
- Total interest: 0.005 × 200,000 × 361 ÷ 2 = $180,500.00; total paid $380,500.00.
- Annuity interest: $1,199.10 × 360 − 200,000 = $231,676.38.
- Saving: $51,176.38.
How to read the result
Equal principal costs less interest overall, but the early payments are much higher: here $1,555.56 versus $1,199.10 for an annuity. Choose it if you can comfortably afford the first payments and expect your income to stay stable or fall, such as near retirement. If cash flow is tight early on, an annuity loan with extra prepayments later can be a middle path.
Common mistakes
- Budgeting for the average payment instead of the high first payment.
- Comparing total interest without considering the cash you could keep earlier with an annuity.
- Assuming the rate is fixed when it is variable.
- Forgetting fees and insurance that are added to the payment.
Frequently asked questions
Equal principal or equal payment?
Equal principal starts higher but costs less interest; equal payment is easier to budget.
What is the total interest formula?
Monthly rate × principal × (N + 1) ÷ 2.
Why does the payment drop every month?
The principal part is fixed while interest falls with the balance.
Sources: Brealey, Myers and Allen, Principles of Corporate Finance (loan amortization)