Premium Payment Calculator
Find a fixed monthly payment that zeroes the balance by your target payoff month under a minimum-interest rule. View full amortization and export results.
Inputs
Installments start from month 2; ensure the balance reaches 0 by this month-end.
Results
Payment Schedule
| Period | Begin Balance | Interest | Payment | End Balance | Min Interest Applied |
|---|---|---|---|---|---|
| 1 | $1,000.00 | $30.00 | - | $1,030.00 | No |
| 2 | $1,030.00 | $30.90 | $131.11 | $929.79 | No |
| 3 | $929.79 | $27.89 | $131.11 | $826.57 | No |
| 4 | $826.57 | $24.80 | $131.11 | $720.26 | No |
| 5 | $720.26 | $21.61 | $131.11 | $610.75 | No |
| 6 | $610.75 | $18.32 | $131.11 | $497.97 | No |
| 7 | $497.97 | $14.94 | $131.11 | $381.79 | No |
| 8 | $381.79 | $11.45 | $131.11 | $262.14 | No |
| 9 | $262.14 | $7.86 | $131.11 | $138.89 | No |
| 10 | $138.89 | $5.00 | $131.11 | $12.78 | Yes |
How to Use the Premium Payment Calculator (Method and Examples)
What this calculator does: It computes a fixed monthly payment so that the remaining balance reaches zero at the end of your target payoff month, while honoring a minimum-interest-per-month rule. Unlike standard annuity formulas, the minimum interest constraint breaks the closed-form solution, so we use a robust bisection method to solve for the monthly payment.
1) How to Use
- Annual Premium: Enter the total annual premium amount.
- Down Payment Ratio: Enter as a decimal (e.g., 0.166 ≈ 16.6%). The down payment is Annual Premium × Ratio. The initial balance equals Annual Premium − Down Payment.
- Monthly Interest Rate: Enter as a decimal (e.g., 0.03 for 3% per month).
- Minimum Monthly Interest: The smallest interest charged each month; if calculated interest is lower, this minimum applies.
- Total Installments: Number of payment months. Installments start from month 2.
- Target Payoff Month: The month by which balance must be zero (e.g., month 10). Make sure Total Installments ≤ Payoff Month − 1.
- Rounding Method: Choose to round to cents or ceil to cents to control how amounts are displayed and exported.
2) Calculation Method
The engine simulates month-by-month balances under a fixed payment M (unknown). For each month:
- Interest = max(Begin Balance × Monthly Interest Rate, Minimum Monthly Interest). If balance is zero, interest is zero.
- Add interest to the balance.
- From month 2 onward, apply the fixed monthly payment (for a total of Total Installments payments that end exactly at Target Payoff Month).
- Compute End Balance and roll forward.
We determine M via bisection:
- Lower bound = Initial Balance ÷ Total Installments.
- Upper bound = Lower bound + 20 (adjusted upward automatically if needed).
- At each step, simulate to the payoff month:
- If final balance > 0, M is too low → raise lower bound.
- If final balance ≤ 0, M may be high or just right → lower upper bound.
- Repeat until bounds converge or iterations cap, then simulate the final schedule with the found M.
3) Reading the Output
- Fixed Monthly Payment: The solved monthly amount applied from month 2 through the payoff month.
- Payment Schedule: For each month 1..Target Payoff Month:
- Begin Balance, Interest, Payment (if applicable), End Balance, and whether Min Interest Applied.
- Month 1 shows the post-down-payment balance; installments start at month 2.
- Total Interest: Sum of monthly interest over the full horizon.
4) Tips and Scenarios
- If minimum interest frequently applies, the payment required for zero balance may be higher than naive expectations.
- To change the payoff month (e.g., month 11), simply adjust Target Payoff Month and Total Installments (e.g., still 9 installments) and recalculate.
- For auditing or sharing, use Export Excel (CSV) or Export PDF to save the full schedule.
This calculator is designed for clarity and auditability, providing a complete schedule with consistent rounding behavior and export options for internal review or client presentation.