Certified Financial Analyst with expertise in fixed-income securities and consumer lending.
The **Loan Payment Term Calculator** determines the number of months or years required to fully pay off a loan. Input any three variables (Principal Loan Amount, Monthly Payment, Annual Interest Rate, or Term in Months) to solve for the missing one.
Loan Payment Term Calculator
Loan Amortization Formula
The core relationship between Principal ($P$), Monthly Payment ($PMT$), Monthly Rate ($i$), and Term ($N$) is given by the amortization formula:
$$P = PMT \times \left[ \frac{1 – (1 + i)^{-N}}{i} \right]$$
Formula Source: Investopedia – Amortization Formula
Solving for the variables:
P (F) = PMT × [ (1 - (1 + i)^-N) ÷ i ]
PMT (P) = P × [ i(1 + i)^N ÷ ((1 + i)^N - 1) ]
R (V) — Solved Iteratively (Find rate R for matching PMT)
N (Q) = - \frac{\ln\left(1 - \frac{P \times i}{PMT}\right)}{\ln(1 + i)}
Variables Explained
- F (Principal – $P$): The total amount of money initially borrowed.
- P (Monthly Payment – $PMT$): The fixed amount paid monthly toward principal and interest.
- V (Annual Rate – $R$): The nominal annual interest rate applied to the loan, expressed as a percentage.
- Q (Term – $N$): The total number of monthly payments (months) required to pay off the loan.
Related Calculators
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- Amortization Schedule Calculator
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What is a Loan Payment Term?
The **Loan Payment Term ($N$)** is the duration, usually measured in months or years, over which a loan is scheduled to be repaid. The term significantly impacts both the size of the monthly payment and the total amount of interest paid over the life of the loan. A longer term leads to lower monthly payments but results in substantially more interest cost.
Knowing the term is essential for budgeting and comparing loan offers. Lenders use the term, along with the principal and interest rate, to calculate the fixed monthly payment using the amortization formula, ensuring the loan is fully paid down to zero by the end of the term.
How to Calculate Loan Term (Example)
Scenario: Principal ($P$) = $20,000, Monthly Payment ($PMT$) = $400, Annual Rate ($R$) = 6.5%.
- Determine Monthly Interest Rate ($i$):
$$i = 6.5\% \div 12 \div 100 \approx 0.005417$$
- Calculate the Term ($N$):
The term is found by rearranging the amortization formula and solving for $N$ using logarithms. This calculation shows the number of months required to reduce the principal to zero using the given payment and rate.
- Final Result:
In this scenario, the calculated term ($N$) is approximately $\mathbf{55.8}$ months, or just under 4 years and 8 months.
Frequently Asked Questions (FAQ)
A shorter term means you have fewer months to repay the principal. To pay the same principal in less time, the principal portion of your monthly payment must be higher, leading to a larger total monthly payment.
Is the term affected by extra payments?Yes. If you make extra payments toward the principal, the loan balance reduces faster. Since the formula re-amortizes the remaining balance, the effective term of the loan shortens significantly, reducing the total interest paid.
What happens if the monthly payment ($PMT$) is too low?If the monthly payment is less than the monthly accrued interest (i.e., $PMT < P \times i$), the loan balance will actually increase, leading to negative amortization and making the loan term infinite (it will never be paid off).
How do I convert months to years?To convert the term from months to years, simply divide the number of months by 12. For example, 60 months is equal to 5 years.