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Cumulative Principal Paid

Cumulative Principal Paid

Total principal repaid over the first p payments: the original loan less the balance still outstanding after payment p.

When to use: Use to measure how much equity you have built in a financed asset, or how far through a loan you really are, which is not the same as the fraction of payments made.

Calculator

Formula

P1..p=PVBpP_{1..p} = PV - B_p

Variables

SymbolNameDescriptionUnit
CumPrincipalCumulative PrincipalPrincipal repaid through payment p$
PVOriginal LoanOriginal loan amount$
PMTPaymentPeriodic payment amount$
kInterest RateAnnual interest rate%
mPayments per YearNumber of payments per yearinteger
pPayments MadeNumber of payments already madeinteger

Real-Life Examples

Example 1: Five Years into a Mortgage

A $300,000 mortgage at 6.5% with monthly payments of $1,896.20. How much principal has been repaid after 60 payments?

Given

PV = $300,000.00PMT = $1,896.20k = 6.5000%m = 12.00p = 60.00

Step-by-Step

1.Remaining balance after 60 payments ≈ $280,833.22
2.Cumulative principal = 300,000 − 280,833.22
3.Cumulative principal ≈ $19,166.78
Result:$19,166.78

After a sixth of the term, only 6.4% of the loan has been repaid. Most of the first five years of payments went to interest.

Example 2: First Year of an Auto Loan

A $25,000 car loan at 7% over 5 years, $495.03 per month. Principal repaid after 12 payments?

Given

PV = $25,000.00PMT = $495.03k = 7.0000%m = 12.00p = 12.00

Step-by-Step

1.Remaining balance after 12 payments ≈ $20,672.55
2.Cumulative principal = 25,000 − 20,672.55
3.Cumulative principal ≈ $4,327.45
Result:$4,327.45

A fifth of the payments have been made and about 17% of the loan repaid. Shorter loans at moderate rates keep interest and principal closer together.

Frequently Asked Questions

It is the part of your equity that came from repaying the loan. Equity also changes with the asset's market value, which this formula does not track.

Every payment is split entirely between interest on the outstanding balance and reduction of that balance, so the two running totals always add up to the total paid.