Mr. Chen is a Chartered Financial Analyst with deep expertise in fixed-income securities and loan amortization, ensuring the precise calculation of principal and interest payments.
The **Monthly Payment Calculator** uses the loan amortization formula to determine the required Principal and Interest (P&I) payment. It can solve for any missing variable: Monthly Payment (M), Principal (P), Annual Rate (R), or Loan Term (T), provided you enter the other three.
Loan Monthly Payment Calculator (P&I Only)
*Assumes monthly payments (12 periods per year).
Monthly Payment Formulas
The core P&I (Principal and Interest) payment ($M$) is calculated using the loan amortization formula:
$$ M = P \frac{i(1+i)^n}{(1+i)^n - 1} $$
Where $i$ is the monthly interest rate ($R/1200$) and $n$ is the total number of periods ($T \times 12$).
Formula Source: Investopedia (Amortization)
Variables Explained
- M (Monthly Payment): The fixed amount paid monthly to cover principal and interest. (F in input map)
- P (Principal Amount): The initial amount borrowed. (P in input map)
- R (Annual Interest Rate): The annual percentage rate of the loan. (V in input map)
- T (Loan Term in Years): The duration of the loan in years. (Q in input map)
Related Calculators
Analyze your loan affordability and long-term costs:
- Loan Affordability Calculator
- Total Interest Paid Calculator
- Loan Term Calculator (Solving for T)
- Home Equity Loan Calculator
What is a Monthly Payment (P&I)?
The **Monthly Payment** calculated here is the **Principal and Interest (P&I)** portion of a fully amortizing loan, such as a mortgage or auto loan. This fixed payment amount is designed to fully pay off the loan (principal) and cover the interest accrued over the life of the loan by the end of the specified term (T).
The calculation is complex because the interest portion decreases every month as the principal balance decreases. Initially, the majority of the monthly payment goes toward interest. Over time, as the principal balance shrinks, a larger portion of the fixed monthly payment is allocated to the principal, accelerating the payoff.
Understanding this P&I amount is the first step in determining true housing affordability, as it sets the baseline cost before factoring in escrow components like property taxes, homeowners insurance, and private mortgage insurance (PMI).
How to Calculate Monthly Payment (Example)
Let’s calculate the **Monthly Payment (M)** for a \$250,000 loan at 4.5% interest over 15 years.
- Determine Parameters:
$P = \$250,000$. $R = 4.5\%$. $T = 15$ years.
Monthly rate $i = 0.045 / 12 = 0.00375$. Total payments $n = 15 \times 12 = 180$.
- Calculate Amortization Factor:
Factor $= \frac{i(1+i)^n}{(1+i)^n – 1} = \frac{0.00375(1.00375)^{180}}{(1.00375)^{180} – 1} \approx 0.007650$
- Calculate Monthly Payment (M):
$M = P \times \text{Factor} = \$250,000 \times 0.007650 \approx \$1,912.50$.
- Conclusion:
The required Monthly Payment (M) is approximately \$1,912.50.
Frequently Asked Questions (FAQ)
No, this calculator only determines the Principal and Interest (P&I) portion of the payment. For a full PITI payment (Principal, Interest, Taxes, Insurance), please use our Mortgage Payment Calculator.
Q: How does the loan term (T) affect the monthly payment (M)?A shorter loan term (e.g., 15 years vs 30 years) results in a significantly higher Monthly Payment (M), but saves a substantial amount on Total Interest Paid over the life of the loan.
Q: Can I solve for the Principal (P) if I know M, R, and T?Yes. The formula can be rearranged to solve for Principal: $P = M \frac{(1+i)^n – 1}{i(1+i)^n}$. This tells you the maximum loan you can afford for a given monthly budget.
Q: What if the annual interest rate (R) is 0%?If $R = 0\%$, the interest $i=0$. The monthly payment is simply $M = P / n$. Our calculator handles this case by treating the payment as straight principal division.