Mortgage or Home Loan Calculator

Amortized Loan Calculator: Paying Back a Fixed Amount Periodically

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

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