Simple Interest Calculator With Extra Payments

This simple interest calculator with extra payments estimates how much interest accrues on a loan when you make additional payments, using a daily simple-interest model. Enter the balance, annual interest rate, regular monthly payment, and extra amount; it returns the estimated payoff time, total paid, and interest paid.

Formula

The calculator uses a monthly-rate approximation to estimate repayment. It treats the annual percentage rate (APR) divided by 12 as the interest rate per month, and assumes the combined regular and extra payment is made at the end of each month.

n = ceil(round(−ln(1 − r × B ÷ M) ÷ ln(1 + r), 6))

• B is the starting loan balance in dollars.
• APR is the annual interest rate entered as a percentage.
• r is the monthly rate, APR ÷ 1200.
• M is the total monthly payment: regular payment plus extra payment, in dollars.
• n is the estimated number of monthly payments, rounded up to a whole month.

Estimated total paid is M × n. Estimated interest paid is total paid minus the starting balance. This whole-month method assumes the same payment in every month, including the final month, so it may overstate the actual last payment. It is a simplified estimate, not a daily accrual ledger.

Worked Example

Using the calculator’s defaults: balance B = $20,000, APR = 8%, regular payment = $500, and monthly extra payment = $100.

1. Combine the payments: M = $500 + $100 = $600 per month.
2. Convert the APR to a monthly rate: r = 8 ÷ 1200 = 0.0066667.
3. Estimate months: n = ceil[round(−ln(1 − 0.0066667 × 20,000 ÷ 600) ÷ ln(1.0066667), 6)] = ceil(37.51) = 38 months.
4. Estimate total paid: $600 × 38 = $22,800.
5. Estimate interest: $22,800 − $20,000 = $2,800.

The displayed estimates are therefore 38 months, $22,800 total paid, and $2,800 interest. The assumed final $600 payment is not adjusted downward to match the remaining amount due.

Assumptions

• Fixed annual rate for the entire payoff period.
• Payments arrive at the end of each month; the extra amount is paid every month.
• Interest is approximated using monthly compounding at APR ÷ 12, rather than calculated from exact daily balances.
• Fees, taxes, insurance, penalties, and any lender-specific payment allocation are not included.

How Simple Interest and Extra Payments Work

Simple interest is calculated on the outstanding principal rather than on previously accrued interest. With a loan that accrues interest daily, the lender generally calculates interest using the balance and the number of days in the period. Paying principal earlier can therefore reduce the balance on which later interest accrues. The precise calculation depends on the contract and payment dates.

An extra payment can reduce the balance faster if it is applied to principal. But an additional amount may instead be treated as an advance toward a future scheduled payment, or be allocated according to the account’s terms. The calculator assumes the entire extra amount joins the regular monthly payment and reduces what is owed. Check the lender’s statement or ask how an extra payment is applied.

Simple interest is not the same as a loan with a fixed monthly installment calculated by a standard amortization formula. A calculator that assumes daily interest needs more detail—such as the dates of payments and the day-count convention—to reproduce a lender’s exact ledger. This tool provides a consistent estimate from monthly inputs.

How to Use and Read the Estimate

• Enter the current principal balance, not necessarily the original amount borrowed. Use the latest lender balance when available.
• Enter the APR as a percentage number: for example, enter 8 for 8%, not 0.08.
• Enter the regular monthly amount and the extra amount you expect to pay each month. Enter zero if there is no extra payment.
• Compare the estimated months, total paid, and interest with the same inputs but an extra payment of zero. The difference is a mathematical illustration under the stated assumptions, not a promise of lender results.

The month count is rounded upward because a loan generally cannot be cleared by a fraction of a scheduled monthly payment in this simplified model. Since the tool counts a full combined payment in every month, total paid and interest may be higher than an estimate that calculates a smaller final payment. It also does not show the balance after each individual payment.

Limits and Common Mistakes

The model requires a positive monthly payment and assumes it exceeds the interest accruing under its monthly-rate approximation. If the payment does not cover interest, the balance will not be repaid by this formula; the displayed calculation is not meaningful for that case. A payment close to the interest amount can also produce a very long payoff estimate.

Common sources of mismatch include entering the original loan amount instead of the current balance, confusing a monthly payment with a biweekly amount, entering APR as a decimal, and assuming all extra money goes directly to principal. Actual interest may differ because of daily accrual, payment timing, changing rates, fees, or irregular extra payments. For a useful comparison, keep the balance, rate, and regular payment the same and change only the extra amount.

Frequently Asked Questions

Does an extra payment reduce simple interest?
It can reduce later interest if it lowers the principal balance sooner. The effect depends on when the payment arrives and how the lender applies it.

Should I enter the extra payment once or every month?
This calculator treats the extra amount as recurring each month. For a one-time payment or irregular extras, its month and balance estimates will not represent that schedule.

Why does the calculator use APR divided by 12?
That converts an annual percentage rate into a monthly-rate approximation for this formula. A lender’s daily simple-interest calculation may use actual days and a different convention.

Can I use this for a loan with changing rates?
No. The formula assumes one fixed APR throughout repayment. A rate change requires recalculating with the applicable rates and periods.

Why is the estimated final payment the same as the others?
The tool rounds the payoff time up to a whole month and multiplies that count by the full monthly amount. The actual final payment may be smaller, depending on accrued interest and the lender’s balance calculation.

This result is an estimate, and the lender’s disclosure gives the exact figures.

Related

• How to Find r in Simple Interest
• How T-Bill Interest Is Paid and What to Expect
• Express Interest: Calculate Loan Interest Costs

in bal | Starting loan balance | $ | 20000 | 0.01 | 100000000
in apr | Interest rate (APR) | % | 8 | 0.01 | 100
in pmt | Regular monthly payment | $ | 500 | 0.01 | 100000000
in extra | Extra payment each month | $ | 100 | 0 | 100000000
out months | Estimated months to payoff | months | ceil(round(-ln(1 - (apr / 1200) * bal / (pmt + extra)) / ln(1 + apr / 1200), 6)) | 0
out total | Estimated total paid | $ | (pmt + extra) * months | 2
out int | Estimated interest paid | $ | total - bal | 2