Amortization Formula Solve for N Calculator

Amortization is the process of gradually paying off a loan over time. This calculator helps you determine the number of periods (n) needed to fully repay a loan when you know the monthly payment, interest rate, and principal amount.

What is Amortization?

Amortization is a financial process where the outstanding balance of a loan is reduced over time through regular payments. These payments typically consist of both principal and interest. The amortization schedule shows how much of each payment goes toward the principal and how much goes toward interest over the life of the loan.

Understanding amortization helps borrowers plan their finances, as it shows how quickly they can pay off their debt and how much interest they will pay over time.

Amortization Formula

The amortization formula used to calculate the number of periods (n) is derived from the standard loan payment formula:

P = A × [1 - (1 + r)^-n] / r

Where:

P = Principal loan amount
A = Regular payment amount
r = Interest rate per period (monthly rate = annual rate / 12)
n = Number of periods (months)

To solve for n, we rearrange the formula:

n = -ln(1 - (P × r) / A) / ln(1 + r)

This formula allows you to determine how many payments are needed to fully repay a loan given the principal, payment amount, and interest rate.

How to Use This Calculator

Enter the loan amount (principal) in the first field.
Enter the regular monthly payment amount in the second field.
Enter the annual interest rate in the third field.
Click the "Calculate" button to see the number of periods needed.
Review the result and the amortization schedule chart.

Note: This calculator assumes monthly compounding. For different compounding periods, you would need to adjust the interest rate accordingly.

Example Calculation

Let's say you have a loan of $10,000 with a monthly payment of $250 and an annual interest rate of 6%. Using the calculator:

Enter 10000 for the loan amount.
Enter 250 for the monthly payment.
Enter 6 for the annual interest rate.
Click "Calculate".

The calculator will show that it will take approximately 48 months (4 years) to fully repay the loan.

Amortization Schedule Example
Period	Payment	Principal	Interest	Balance
1	$250.00	$208.33	$41.67	$9,791.67
2	$250.00	$215.29	$34.71	$9,576.38
3	$250.00	$222.55	$27.45	$9,353.83

The table shows the first three payments of the amortization schedule, demonstrating how the principal and interest portions change over time.

FAQ

What is the difference between amortization and depreciation?: Amortization refers to the gradual reduction of a loan's balance over time through regular payments. Depreciation refers to the gradual loss of value of an asset over time.
Can I use this calculator for car loans?: Yes, this calculator can be used for any type of loan, including car loans, as long as you know the principal amount, monthly payment, and interest rate.
What if my loan has a different compounding period?: This calculator assumes monthly compounding. For loans with different compounding periods (e.g., daily, weekly), you would need to adjust the interest rate accordingly.
Is the result always an exact number of months?: The result may not always be a whole number. In such cases, the loan will be fully paid off in the next full period.
Can I use this calculator for mortgages?: Yes, this calculator can be used for mortgages as well, provided you enter the correct principal amount, monthly payment, and interest rate.