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Remaining Balance

Calculates the remaining loan balance after p payments have been made.

When to use: Use to find how much you still owe on a loan after some payments.

Calculator

Formula

B=PV×(1+k)pPMT×(1+k)p1kB = PV \times (1+k)^p - PMT \times \frac{(1+k)^p - 1}{k}

Variables

SymbolNameDescriptionUnit
BRemaining BalanceOutstanding loan balance$
PVOriginal LoanOriginal loan amount$
PMTPaymentPeriodic payment amount$
kInterest RateAnnual interest rate%
pPayments MadeNumber of payments already madeinteger

Real-Life Examples

Example 1: Mortgage Balance

A $200,000 mortgage at 6% with annual payments of $19,264.68. Balance after 5 years?

Given

PV = 200,000PMT = 19,264.68k = 0.06p = 5

Step-by-Step

1.B = $200,000 × (1.06)^5 - $19,264.68 × [(1.06)^5 - 1]/0.06
2.B = $267,645.17 - $19,264.68 × 5.6371
3.B = $267,645.17 - $108,619.28
4.B = $159,025.89
Result:159,048.32

After 5 annual payments, $159,025.89 remains on the mortgage.

Example 2: Business Loan

$50,000 loan at 8% with $7,451.47 annual payments. Balance after 3 payments?

Given

PV = 50,000PMT = 7,451.47k = 0.08p = 3

Step-by-Step

1.B = $50,000 × (1.08)^3 - $7,451.47 × [(1.08)^3 - 1]/0.08
2.B = $62,985.60 - $7,451.47 × 3.2464
3.B = $62,985.60 - $24,189.70
4.B = $38,795.90
Result:38,795.90

$38,795.90 remains after 3 annual payments.

Frequently Asked Questions

Use this formula with the original loan amount (PV), your regular payment (PMT), the interest rate (k), and the number of payments you have made (p). The result is your remaining balance.

Early in a loan, most of each payment goes toward interest because the outstanding balance is large. As you make payments and the balance drops, more of each payment goes to principal, accelerating the balance reduction.

The remaining balance is the principal owed at a point in time. The payoff amount may include accrued interest since the last payment, prepayment penalties, or fees. For a same-day payoff right after a payment, they are typically the same.