Chartered Financial Analyst and expert in debt structuring, amortization, and long-term financial modeling.
The **Loan Term Calculator** determines how long it will take to pay off a loan based on the loan amount, interest rate, and your monthly payment. It can also solve for the missing variable: Loan Principal, Monthly Payment, Annual Rate, or Loan Term (Months).
Loan Term Calculator
Instructions: Enter values for any three of the four parameters (P, F, V, Q) to solve for the missing one.
Loan Parameters
Loan Amortization Formula (Solved for N)
The calculation is based on the standard Amortization formula, rearranged to solve for the number of periods ($N$). Note that $i = R/12$ and $R$ is the annual rate.
Monthly Payment ($M$):
$$M = P \left[ \frac{i(1+i)^N}{(1+i)^N – 1} \right]$$Loan Term (Months, $N$):
$$N = \frac{\log \left(\frac{M}{M – Pi}\right)}{\log(1 + i)}$$ Formula Source: Investopedia: Loan Payment FormulaVariables Explained (P, F, V, Q – Parameters)
- $P$ (Loan Principal): The initial amount borrowed.
- $M$ (Monthly Payment, $F$): The fixed amount paid each month.
- $R$ (Annual Rate, $V$): The annual interest rate of the loan.
- $N$ (Loan Term in Months, $Q$): The total number of monthly payments required to pay off the loan.
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What is Loan Term?
The loan term, also known as the amortization period or tenor, is the length of time specified in the loan agreement during which the borrower must make regular payments to pay off the principal and interest. Terms are typically expressed in months or years (e.g., 30-year mortgage, 60-month car loan). The loan term significantly impacts both the required monthly payment and the total interest paid over the life of the loan.
Generally, a shorter loan term results in higher monthly payments but substantially lower total interest costs. Conversely, a longer loan term offers lower, more manageable monthly payments but means paying significantly more interest over the loan’s lifetime. Finding the optimal loan term is a balance between affordability and minimizing long-term cost.
How to Calculate Loan Term (Example)
You take out a \$20,000 loan ($P$) at 7% Annual Interest ($R$) and plan to pay \$400 per month ($M$). We are solving for $N$ (months):
- Step 1: Calculate the Monthly Interest Rate ($i$)
$i = 7\% / 12 = 0.005833$
- Step 2: Check Viability (Interest portion of payment)
First Month’s Interest: $\$20,000 \times 0.005833 = \$116.67$. Since the Monthly Payment (\$400) is greater than the interest, the loan is viable.
- Step 3: Apply the Loan Term Formula (Solved for $N$)
Substitute values into the formula: $N = \frac{\log \left(\frac{400}{400 – 20000 \times 0.005833}\right)}{\log(1 + 0.005833)}$
- Step 4: Solve for $N$
The calculation yields $N \approx \mathbf{55.84}$ months.
The loan will be paid off in approximately 56 months (4 years and 8 months).
Frequently Asked Questions (FAQ)
The longer the term, the lower the monthly payment, because the principal is stretched over more periods. However, a longer term also means more interest accrues, increasing the total cost.
Usually not directly. To change the term, you typically must either make extra principal payments (which effectively shortens the term) or officially refinance the loan with a new principal, rate, and term.
Amortization is the process of paying off debt over time in regular installments, where each payment covers both interest and a portion of the principal, structured to fully extinguish the debt by the end of the term.
In the US, 30 years (360 months) is the standard maximum. However, 15-year, 20-year, and 25-year terms are also common.