Home Loan Full Settlement Calculator

Loan Balance Equation:

\[ B = P \times \frac{(1 + r)^n - (1 + r)^k}{(1 + r)^n - 1} \]

Principal Amount (P):

USD

Monthly Interest Rate (r):

decimal

Total Months (n):

months

Payments Made (k):

payments

Remaining Balance (B):

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1. What is the Loan Balance Equation?

The loan balance equation calculates the remaining amount to be paid for full settlement of a home loan after making k payments. It accounts for the principal amount, interest rate, and payment history.

2. How Does the Calculator Work?

The calculator uses the loan balance equation:

\[ B = P \times \frac{(1 + r)^n - (1 + r)^k}{(1 + r)^n - 1} \]

Where:

\( P \) — Principal loan amount (USD)
\( r \) — Monthly interest rate (decimal)
\( n \) — Total number of payments (months)
\( k \) — Number of payments already made
\( B \) — Remaining balance (USD)

Explanation: The equation calculates how much principal remains after k payments, accounting for the amortization schedule of the loan.

3. Importance of Loan Balance Calculation

Details: Knowing your remaining balance is crucial when considering loan refinancing, early payoff, or property sale. It helps in financial planning and decision making.

4. Using the Calculator

Tips: Enter the original loan amount, monthly interest rate (as decimal), total loan term in months, and number of payments already made. All values must be valid (principal > 0, rate ≥ 0, months > 0, payments ≥ 0 and ≤ total months).

5. Frequently Asked Questions (FAQ)

Q1: How do I convert APR to monthly rate?
A: Divide the annual percentage rate (APR) by 12 (for months) and by 100 to convert to decimal. Example: 6% APR = 0.06/12 = 0.005 monthly rate.

Q2: Does this include extra payments?
A: No, this calculates the standard amortization schedule. For loans with extra payments, a more detailed amortization table would be needed.

Q3: Why is my remaining balance higher than expected?
A: Early in the loan term, most payments go toward interest rather than principal. The balance decreases slowly at first, then more rapidly later.

Q4: Can I use this for other types of loans?
A: Yes, it works for any amortizing loan with fixed payments (car loans, personal loans, etc.), not just home loans.

Q5: How accurate is this calculation?
A: It's mathematically precise for fixed-rate loans. For adjustable-rate loans, it's accurate only until the next rate adjustment.