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Remaining Loan Balance

The principal still owed after a given number of payments on an amortizing loan: the present value of the payments that remain.

Compounding

Remaining Balance (Annual Compounding)

Outstanding loan balance after p payments. The final payment is capped at the amount owed, and the balance stays zero after payoff. At zero interest, balance is max(0, PV − PMT × p).

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

Calculator

Formula

Bp=max(0,PV×(1+k)pPMT×(1+k)p1k)B_p = \max\left(0, PV \times (1+k)^p - PMT \times \frac{(1+k)^p - 1}{k}\right)

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 = $200,000.00PMT = $19,264.68k = 6.0000%p = 5.00

Step-by-Step

1.Periodic rate = 0.06 / 1 = 0.06
2.For each payment: interest = prior balance × periodic rate; actual payment is capped at prior balance + interest
3.At payment 5: interest ≈ $10,093.19, principal ≈ $9,171.49, remaining balance ≈ $159,048.32
4.B ≈ $159,048.32
Result:$159,048.32

For these inputs, Remaining Balance is $159,048.32 under the stated payment, compounding and accounting assumptions.

Example 2: Business Loan

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

Given

PV = $50,000.00PMT = $7,451.47k = 8.0000%p = 3.00

Step-by-Step

1.Periodic rate = 0.08 / 1 = 0.08
2.For each payment: interest = prior balance × periodic rate; actual payment is capped at prior balance + interest
3.At payment 3: interest ≈ $3,425.68, principal ≈ $4,025.79, remaining balance ≈ $38,795.15
4.B ≈ $38,795.15
Result:$38,795.15

For these inputs, Remaining Balance is $38,795.15 under the stated payment, compounding and accounting assumptions.

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.