Simple vs Compound Interest Loan Calculator Explained

This calculator estimates a fixed-payment loan’s monthly payment and total interest using monthly compounding, then lets you compare that result with the simple-interest calculation for the same principal, rate, and term. Enter the loan amount, annual percentage rate (APR), and term; the outputs are estimates based on the assumptions below, not a lender’s payoff quote.

Formula

The calculator uses the standard level-payment amortization formula, which assumes interest accrues monthly on the unpaid balance. Its first result is the monthly payment:

Payment = P × r ÷ [1 − (1 + r)⁻ⁿ]

• P is the amount borrowed, in dollars.
• r is the monthly interest rate as a decimal: APR ÷ 1200. For an 8% APR, r = 8 ÷ 1200.
• n is the number of monthly payments: loan term in years × 12.

Total interest is calculated as monthly payment × n − P. Because the payment is rounded to cents, the displayed total uses that rounded payment. In actual repayment, the final installment may be adjusted slightly to clear a remaining balance.

“Simple interest” and “compound interest” describe how interest is calculated, not two interchangeable payment formulas. A basic simple-interest calculation for one period is I = P × i × t, where I is interest, P is principal, i is the rate per period, and t is the number of periods. If unpaid interest is added to the balance and future interest is charged on that larger balance, interest compounds. The calculator above models a standard amortizing balance with monthly interest; it is not a separate simple-interest loan calculator.

Worked Example

Using the calculator’s default inputs: loan amount P = $20,000, APR = 8%, and term = 5 years.

1. Convert the APR to a monthly decimal rate: r = 8 ÷ 1200 = 0.0066667.
2. Find the number of monthly payments: n = 5 × 12 = 60.
3. Apply the payment formula: $20,000 × 0.0066667 ÷ [1 − (1.0066667)⁻⁶⁰] = approximately $405.53 per month, rounded to cents.
4. Calculate total interest using the rounded payment: $405.53 × 60 − $20,000 = $4,331.80.

These figures are the calculator’s arithmetic outputs for the defaults. A loan schedule that adjusts the last payment or uses different payment dates can produce a slightly different final total.

Assumptions

• The rate is fixed for the full term.
• Payments are equal, made monthly, and made at the end of each period.
• Interest compounds monthly at APR ÷ 12.
• Fees, taxes, insurance, PMI, escrow, late payments, and extra payments are not included.

When Simple and Compound Interest Apply

Simple interest is often used to describe interest calculated only on the original principal over a stated period. For example, if $1,000 accrues 6% simple interest for one year, the interest is $60. If the $60 is retained in the balance and earns interest in the next period, the calculation has a compounding effect: future interest applies to principal plus accumulated interest.

For an amortizing loan, each payment generally covers the interest due for that period and reduces principal by the remainder. The next period’s interest is calculated on the then-outstanding balance. That changing balance is why multiplying the original principal by APR and years does not usually give the total interest on a regularly paid loan. The payment formula accounts for the principal shrinking over time.

Some contracts calculate interest daily or use other schedules. “Simple interest” in a contract may mean interest is calculated on the current outstanding principal rather than on previously accrued interest; it does not necessarily mean the borrower pays one flat amount of interest for the entire term. Check the lender’s disclosure for the actual method, accrual dates, and payment schedule.

How to Read the Comparison

Use the calculator’s monthly payment as the scheduled amount under its assumptions, and use total interest to see the estimated interest paid across all scheduled installments. Compare like with like: keep principal, annual rate, payment frequency, and term consistent. A comparison that changes the term or the timing of payments is not isolating the effect of simple versus compound interest.

If you want a simple-interest reference figure for one fixed interval, use I = P × i × t, making sure the rate and time use the same unit. For instance, an annual rate must be paired with time in years. That figure is not a substitute for an amortization schedule, since it does not represent the effect of monthly principal reductions.

Common Problems and Limits

• Using APR as a monthly rate: The calculator converts annual percentage APR to a monthly decimal by dividing by 1200. Enter 8 for 8%, not 0.08.
• Mixing up interest and total repayment: Total repayment includes the principal borrowed; total interest is the amount above principal under the modeled schedule.
• Ignoring fees or other charges: The calculator has no fee input. A stated APR or payment may include or exclude costs depending on the loan disclosure, so use the lender’s figures when reconciling estimates.
• Assuming every contract compounds monthly: Actual accrual and payment rules can differ. Daily accrual, irregular dates, variable rates, skipped payments, and extra payments are not represented.
• Rounding differences: Payments are shown to cents, while lenders may calculate interest at finer precision and adjust a final installment. Small differences can accumulate.

The formula also assumes the full term is repaid through level monthly payments and a positive APR. It does not calculate a variable-rate schedule, a payoff quote for a particular date, or the total cost of borrowing with unentered charges.

Frequently Asked Questions

Is a loan payment calculated with simple or compound interest?
It depends on the contract’s interest method and payment schedule. This calculator assumes monthly interest on the outstanding balance, with scheduled payments reducing that balance over time.

Does simple interest mean no interest is charged on interest?
In a basic simple-interest calculation, interest is based on principal rather than previously accumulated interest. Contract terminology and accrual mechanics can vary, so review the lender’s disclosed method.

Why is multiplying the loan amount by APR and years inaccurate?
That calculation treats the original principal as if it remained unchanged for the whole term. Regular payments reduce the balance, so the amortization formula calculates interest period by period on a declining balance.

Can I use this calculator for a variable-rate loan?
Only as a fixed-rate illustration for the APR entered. It cannot forecast rate changes or recalculate a payment schedule after a change.

Why might the lender’s payment differ from this result?
Possible reasons include fees, a different interest-accrual method, payment dates, rounding, or an adjusted final payment. Compare the calculator’s assumptions with the lender’s disclosure.

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

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in p | Loan amount | $ | 20000 | 1 | 100000000
in apr | Interest rate (APR) | % | 8 | 0.01 | 100
in yrs | Loan term | years | 5 | 0.0833 | 50
out pmt | Monthly payment | $ | p * (apr / 1200) / (1 - (1 + apr / 1200) ^ -(yrs * 12)) | 2
out int | Total interest | $ | pmt * yrs * 12 - p | 2