Loan Repayment Calculator Remaining Balance

Remaining Balance Formula:

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

Principal (P):

Monthly Interest Rate (r):

decimal

Total Term (n):

months

Months Paid (p):

months

Remaining Balance (B):

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1. What is the Remaining Balance Formula?

The remaining balance formula calculates how much of the principal is still owed on a loan after a certain number of payments have been made. It accounts for both the principal and interest components of each payment.

2. How Does the Calculator Work?

The calculator uses the remaining balance formula:

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

Where:

\( B \) — Remaining balance
\( P \) — 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 how much principal would remain after p payments of an n-payment loan at interest rate r.

3. Importance of Loan Balance Calculation

Details: Knowing your remaining balance helps with refinancing decisions, understanding equity, and planning for early payoff. It's essential when considering selling an asset or restructuring debt.

4. Using the Calculator

Tips: Enter the original loan amount, monthly interest rate (as a decimal), total term in months, and number of payments already made. All values must be positive, and payments made cannot exceed total term.

5. Frequently Asked Questions (FAQ)

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

Q2: Does this work for any loan type?
A: This formula works for standard amortizing loans (fixed rate, fixed payment). It doesn't work for interest-only loans or adjustable-rate mortgages.

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

Q4: How accurate is this calculation?
A: It's mathematically precise for fixed-rate loans. For variable-rate loans, it's accurate only if rates haven't changed.

Q5: Can I use this for extra payments?
A: This assumes regular payments only. For loans with extra payments, you'd need a more complex amortization schedule.