Skip to content
SnapFi

Remaining Balance

Remaining balance after p payments with periodic compounding.

When to use: Use for monthly loan balances (mortgages, car loans).

Calculator

Formula

B=PV×(1+km)p−PMT×(1+km)p−1kmB = PV \times \left(1+\frac{k}{m}\right)^p - PMT \times \frac{\left(1+\frac{k}{m}\right)^p - 1}{\frac{k}{m}}

Variables

SymbolNameDescriptionUnit
BRemaining BalanceOutstanding balance$
PVOriginal LoanOriginal loan amount$
PMTPaymentPeriodic payment$
kInterest RateNominal annual rate%
mPeriods/YearPayments per yearinteger
pPayments MadeNumber of payments madeinteger

Real-Life Examples

Example 1: Monthly Mortgage Balance

$300,000 mortgage at 6% monthly, payment $1,798.65. Balance after 60 payments (5 years)?

Given

PV = 300,000PMT = 1,798.65k = 0.06m = 12p = 60

Step-by-Step

1.B = $300,000 × (1.005)^60 - $1,798.65 × [(1.005)^60 - 1]/0.005
2.B = $300,000 × 1.34885 - $1,798.65 × 69.7700
3.B = $404,656.10 - $125,466.19
4.B = $279,189.91
Result:279,189.91

After 5 years of monthly payments, $279,189.91 remains on the mortgage.

Example 2: Car Loan Balance

$25,000 car loan at 5% monthly, payment $471.78. Balance after 24 payments?

Given

PV = 25,000PMT = 471.78k = 0.05m = 12p = 24

Step-by-Step

1.r = 0.05/12 = 0.004167
2.B = $25,000 × (1.004167)^24 - $471.78 × [(1.004167)^24 - 1]/0.004167
3.B = $27,616.47 - $11,880.89
4.B = $15,735.58
Result:15,741.32

$15,735.58 remains on the car loan after 2 years.

Frequently Asked Questions

Enter the original loan amount as PV, your monthly payment as PMT, the annual rate as k, 12 for m, and the number of monthly payments made as p. The formula calculates what you still owe after those payments.

Home equity equals your property's current market value minus the remaining mortgage balance. Use this formula to find the remaining balance, then subtract it from your home's estimated value.

Yes. By adjusting the payment amount (PMT) upward and calculating the balance at different points, you can see how extra payments accelerate principal reduction and help you decide the most effective overpayment strategy.

Interest Portion of Payment