Amortization Calculator

1. What is the Amortization Calculator?

Definition: The Amortization Calculator computes the monthly payment and remaining balance for an amortized loan, such as a mortgage or car loan, based on the loan amount, interest rate, and term.

Purpose: This tool helps borrowers understand their monthly payment obligations and track the remaining balance over time, aiding in financial planning and loan management.

2. How Does the Calculator Work?

The calculator uses the following formulas:

$ P = A \times \frac{i}{1 - (1 + i)^{-t}} $

$ B = A \times (1 + i)^t - \frac{P}{i} \times ((1 + i)^t - 1) $

Where:

$ P $: Monthly payment ($);
$ A $: Loan amount ($);
$ i $: Monthly interest rate (annual rate / 12);
$ t $: Total number of payments (years × 12);
$ B $: Unpaid balance ($).

Steps:

Enter the loan amount, annual interest rate, loan term, and optional number of payments made.
Convert the annual interest rate to a monthly rate (divide by 12).
Calculate total payments (loan term × 12).
Compute the monthly payment using the repayment formula.
If payments made is provided, compute the remaining balance using the unpaid balance formula.
Display results in currency format with two decimal places.

3. Importance of the Amortization Calculation

Calculating amortization is essential for:

Budgeting: Helps borrowers plan monthly payments to ensure affordability.
Loan Tracking: Allows tracking of the remaining balance to assess prepayment or refinancing options.
Financial Planning: Supports informed decisions about loan terms and interest rates to minimize total costs.

4. Using the Calculator

Example: Calculate the monthly payment and remaining balance for a $10,000 loan with a 6% annual interest rate over 5 years, after 36 payments:

Loan Amount: $10,000; Interest Rate: 6% (0.06); Term: 5 years; Payments Made: 36;
Monthly Rate: $ 0.06 / 12 = 0.005 $; Total Payments: $ 5 \times 12 = 60 $;
Monthly Payment: $ P = 10000 \times \frac{0.005}{1 - (1 + 0.005)^{-60}} \approx 193.33 $;
Remaining Balance after 36 payments: $ B = 10000 \times (1 + 0.005)^{36} - \frac{193.33}{0.005} \times ((1 + 0.005)^{36} - 1) \approx 4604.11 $;
Result: Monthly Payment: $193.33; Remaining Balance: $4604.11.

5. Frequently Asked Questions (FAQ)

Q: What is an amortized loan?
A: An amortized loan is repaid in fixed monthly payments that cover both principal and interest, gradually reducing the balance over the loan term.

Q: Why is the remaining balance useful?
A: Knowing the remaining balance helps borrowers decide whether to refinance, make extra payments, or assess the cost of paying off the loan early.

Q: Can this calculator handle 0% interest loans?
A: Yes, the calculator handles 0% interest by dividing the loan amount by the number of payments for the monthly payment.