David is a Chartered Financial Analyst and a former loan officer with over 15 years of experience in consumer and commercial credit structuring.
This 4-in-1 Loan Repayment calculator helps you understand any amortized loan. Enter any three values—Loan Amount, Annual Rate, Term, or Monthly Payment—and we will solve for the fourth.
Loan Repayment Calculator
Loan Repayment (Amortization) Formulas
i = R / 12 / 100 (Monthly Rate)
n = T * 12 (Number of Months)
Solve for Monthly Payment (M):
M = P * [ i(1 + i)^n ] / [ (1 + i)^n – 1 ]
Solve for Loan Amount (P):
P = M * [ (1 + i)^n – 1 ] / [ i(1 + i)^n ]
Solve for Term (n):
n = log( M / (M – P*i) ) / log(1 + i)
Solve for Rate (i):
(No direct formula; solved iteratively)
Formula Variables
- (P) Loan Amount: The initial principal amount borrowed.
- (R) Annual Rate: The Annual Percentage Rate (APR) for the loan.
- (T) Loan Term: The total number of years to repay the loan (e.g., 5, 15, 30).
- (M) Monthly Payment: The fixed monthly payment to repay the loan in full.
Related Calculators
- Mortgage Payment Calculator
- Auto Loan Calculator
- Personal Loan Calculator
- Loan Amortization Calculator
What is a Loan Repayment Calculator?
A loan repayment calculator is a versatile tool that uses the standard amortization formula to model any type of installment loan. This includes mortgages, auto loans, personal loans, and student loans. An installment loan is defined by a fixed principal amount, a fixed interest rate, and a fixed repayment term, resulting in a fixed monthly payment.
This calculator helps you answer the most important questions about a loan *before* you sign. By entering the loan amount, rate, and term, you can instantly see the monthly payment and determine if it fits your budget. This prevents the common pitfall of agreeing to a loan based only on a “low monthly payment” without understanding the total cost.
This 4-in-1 calculator is especially powerful because it works in reverse. If you know the monthly payment you can afford (M), you can solve for the Loan Amount (P) to see how much you can borrow. You can also solve for the Term (T) to see how much faster you could pay off a loan by adding extra to your payment, or solve for the Rate (R) to compare different lender offers.
How to Calculate Loan Repayment (Example)
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Identify Loan Variables
You are taking out a loan for home improvements:
• Loan Amount (P): $25,000
• Annual Rate (R): 8.5%
• Loan Term (T): 10 years -
Convert to Monthly Terms (i, n)
The formula uses monthly values:
• Monthly Rate (i): 8.5% / 12 / 100 = 0.0070833
• Number of Months (n): 10 years * 12 = 120 -
Choose the Payment Formula
Use the standard formula to solve for Monthly Payment (M):
M = P * [ i(1 + i)^n ] / [ (1 + i)^n – 1 ] -
Calculate the Monthly Payment
Plug in the monthly values:
• Numerator: 0.0070833 * (1 + 0.0070833)^120 = 0.016528
• Denominator: (1 + 0.0070833)^120 – 1 = 1.3340
M = $25,000 * [ 0.016528 / 1.3340 ]
M = $25,000 * 0.01239 = $309.75
Your monthly loan repayment will be $309.75.
Frequently Asked Questions (FAQ)
What is Amortization?
Amortization is the process of paying off a loan over time with regular, fixed payments. In the beginning of the loan, a larger portion of your payment goes toward interest. As you pay down the principal, the interest portion decreases and the principal portion increases, until the loan is fully paid off at the end of the term.
How can I pay my loan off faster?
The easiest way is to pay more than the minimum Monthly Payment (M). Any extra money you pay is typically applied directly to the principal (P), which reduces the loan balance faster and saves you significant money on interest. You can use this calculator to see the effect: solve for (T) using your regular payment, then solve for (T) again with a higher payment.
What is the difference between APR (R) and Interest Rate?
The “interest rate” (or “note rate”) is the cost of borrowing the money. The “Annual Percentage Rate” (APR) includes the interest rate *plus* any origination fees, points, or other lender charges, expressed as an annual percentage. The APR is the most accurate way to compare the true cost of two different loan offers.
What is a “simple interest” loan?
A simple interest loan (like a mortgage or auto loan) calculates interest based on the *current* principal balance. A “precomputed” interest loan calculates all interest upfront, meaning you save no money by paying it off early. This calculator uses the simple interest (amortization) formula, which is the most common type of loan.