Mortgage Payment Calculator Remaining Balance Formula

Remaining Balance Formula:

\[ \text{Balance} = P \times \frac{(1 + r)^n - (1 + r)^p}{(1 + r)^n - 1} \]

Principal (P):

Monthly Interest Rate (r):

decimal

Total Term (n):

months

Months Paid (p):

months

Remaining Balance:

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1. What is the Remaining Balance Formula?

The remaining balance formula calculates how much principal is left on a loan after a certain number of payments. It accounts for the compounding interest and principal payments made over time.

2. How Does the Calculator Work?

The calculator uses the remaining balance formula:

\[ \text{Balance} = P \times \frac{(1 + r)^n - (1 + r)^p}{(1 + r)^n - 1} \]

Where:

\( P \) — Original principal amount
\( r \) — Monthly interest rate (annual rate ÷ 12)
\( n \) — Total number of payments (loan term in months)
\( p \) — Number of payments already made

Explanation: The formula calculates the remaining balance by comparing the total loan term with the payments already made, accounting for interest compounding.

3. Importance of Balance Calculation

Details: Knowing your remaining balance helps with refinancing decisions, prepayment planning, and understanding your equity position. It's essential for financial planning and loan management.

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 positive numbers.

5. Frequently Asked Questions (FAQ)

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

Q2: Does this work for any type of loan?
A: This formula works for standard amortizing loans (like mortgages and car loans) with fixed rates and equal monthly payments.

Q3: Why does my balance decrease slowly at first?
A: Early payments are mostly interest. As the principal decreases, more of each payment goes toward principal.

Q4: How can I pay off my loan faster?
A: Making extra principal payments reduces the balance faster and decreases total interest paid.

Q5: What's the difference between balance and payoff amount?
A: Payoff amount may include additional interest if paying between due dates, while balance shows principal remaining.