Amortized Loan Calculator

Amortized Loan Calculator

Calculate monthly payments, total interest, and amortization schedules for mortgages, auto loans, and home loans instantly.

Loan Principal (INR):	CurrencyINRUSDEUR
Interest Rate APR(%):	%
Loan Term:	yrs mo
	Calculate

Guide: How to Calculate a Monthly Mortgage Payment

Also available as: Home Loan Calculator • Loan Payment Calculator • Monthly Mortgage Calculator

Use Cases

This amortized loan calculator is commonly used for mortgage calculations, auto loan payments, home equity loans, student loans, and any fixed-rate loan with regular payments.

What is an Amortized Loan?

An amortized loan is a loan with scheduled periodic payments of both principal and interest, designed to pay off the loan in full by the end of the term.

Formulas

1. Payment Amount (Per Period)

The payment for an amortized loan is calculated using:

$$P = \frac{r \cdot PV}{1 - (1 + r)^{-n}}$$

Where:

• $P$ = Payment amount per period
• $PV$ = Present value (loan principal)
• $r$ = Interest rate per period
• $n$ = Total number of payments

Converting Annual Rate to Period Rate:

• Daily: $r = \frac{APR}{365}$
• Monthly: $r = \frac{APR}{12}$
• Quarterly: $r = \frac{APR}{4}$
• Yearly: $r = APR$
• Custom (every $x$ days): $r = \frac{APR \cdot x}{365}$

Math.js Expression:

loan_principal = 200000;
annual_rate = 0.06;
monthly_rate = annual_rate / 12;
num_payments = 360;

payment_per_period = (monthly_rate * loan_principal) / (1 - (1 + monthly_rate)^-num_payments);
payment_per_period

2. Total Interest

The total interest paid over the life of the loan:

$$\text{Total Interest} = (P \cdot n) - PV$$

Where:

• $P$ = Payment amount per period
• $n$ = Total number of payments
• $PV$ = Original loan principal

Math.js Expression:

payment = 1199.10;
num_payments = 360;
loan_principal = 200000;

total_interest = (payment * num_payments) - loan_principal;
total_interest

3. Number of Payments

From Loan Term (Most Common):

Calculate the total number of payments based on the loan term:

• Daily payments: $n = \text{Loan Term (years)} \times 365$
• Monthly payments: $n = \text{Loan Term (years)} \times 12$
• Quarterly payments: $n = \text{Loan Term (years)} \times 4$
• Yearly payments: $n = \text{Loan Term (years)}$
• Every $x$ days: $n = \frac{\text{Loan Term (years)} \times 365}{x}$

Math.js Expression:

loan_term_years = 30;
payments_per_year = 12;

num_payments = loan_term_years * payments_per_year;
num_payments

From Payment Amount (Reverse Calculation):

If you know the payment amount and want to calculate how many payments are needed:

$$n = \frac{-\log(1 - \frac{r \cdot PV}{P})}{\log(1 + r)}$$

Where:

• $n$ = Number of payments
• $r$ = Interest rate per period
• $PV$ = Loan principal
• $P$ = Payment amount per period

Math.js Expression:

loan_principal = 200000;
annual_rate = 0.06;
monthly_rate = annual_rate / 12;
payment = 1199.10;

num_payments = -log(1 - (monthly_rate * loan_principal) / payment) / log(1 + monthly_rate);
num_payments

4. Final Payment Amount

If the number of payments results in a fractional value, the final payment will be different:

$$\text{Final Payment} = \text{Remaining Balance} \cdot (1 + r)$$

Where the remaining balance after $n-1$ payments is:

$$\text{Remaining Balance} = PV \cdot (1 + r)^{n-1} - P \cdot \frac{(1 + r)^{n-1} - 1}{r}$$

Math.js Expression:

loan_principal = 200000;
annual_rate = 0.06;
monthly_rate = annual_rate / 12;
payment = 1199.10;
full_payments = 360;

remaining_balance = loan_principal * (1 + monthly_rate)^full_payments - payment * ((1 + monthly_rate)^full_payments - 1) / monthly_rate;
final_payment = remaining_balance * (1 + monthly_rate);
final_payment

Example Calculation

Loan Details:

• Loan Amount: $500,000
• Loan Term: 10 years
• Interest Rate: 6% APR
• Payment Frequency: Monthly

Step 1: Calculate Number of Payments

loan_term_years = 10;
payments_per_year = 12;

num_payments = loan_term_years * payments_per_year;
num_payments

Step 2: Calculate Monthly Payment

loan_principal = 500000;
annual_rate = 0.06;
monthly_rate = annual_rate / 12;
num_payments = 120;

payment_per_period = (monthly_rate * loan_principal) / (1 - (1 + monthly_rate)^-num_payments);
payment_per_period

Step 3: Calculate Total Interest

payment_per_period = 5551.23;
num_payments = 120;
loan_principal = 500000;

total_interest = (payment_per_period * num_payments) - loan_principal;
total_interest

Examples

• $200,000 loan at 6$1,199/month payment (total interest: $231,676)
• $500,000 loan at 6$5,551/month payment (total interest: $166,147)
• $30,000 auto loan at 4$553/month payment (total interest: $3,175)
• $150,000 loan at 5$1,186/month payment (total interest: $63,509)

Example Amortization Schedule (First 3 Payments)

Example loan: $200,000, 6% APR, 30 years (monthly payments).

Payment #	Payment	Interest	Principal	Remaining Balance
1	$1,199.10	$1,000.00	$199.10	$199,800.90
2	$1,199.10	$999.00	$200.10	$199,600.80
3	$1,199.10	$998.00	$201.10	$199,399.70

Note: values are rounded to cents for readability, so totals may differ slightly from a full precision schedule.

Common Mistakes & Tips

Not Shopping for Better Rates: A 0.5% rate difference on a $200,000 mortgage can save over$20,000 in interest over 30 years. Always compare lenders.

Ignoring Total Interest: Focus on total loan cost, not just monthly payment. Longer terms mean lower payments but much higher total interest.

Missing Extra Payment Opportunities: Even one extra payment per year can shorten a 30-year mortgage by 4-5 years and save tens of thousands in interest.

Confusing APR and Interest Rate: APR includes fees and closing costs. Use the actual interest rate for payment calculations, but compare loans using APR.

Frequently Asked Questions

How is a monthly mortgage payment calculated?

Monthly payment is calculated using the loan amount, interest rate divided by 12, and total number of monthly payments. The formula ensures the loan is fully paid by the end of the term.

Can I pay off my loan early?

Most loans allow early payoff, but check for prepayment penalties. Extra payments reduce principal and can save significant interest over time.

What’s the difference between a 15-year and 30-year mortgage?

15-year mortgages have higher monthly payments but much lower total interest. 30-year mortgages offer lower payments but cost significantly more over time.

How much can I afford to borrow?

Lenders typically suggest monthly payments no more than 28-30% of gross monthly income. Use this calculator to find payments that fit your budget.

Does this calculator include property taxes and insurance?

No, this calculates principal and interest only. Add property taxes, insurance, and HOA fees separately for total monthly housing cost.

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