Principal Portion of Payment

Calculates how much of a specific loan payment goes toward reducing the principal balance. Equals the total payment minus that payment's interest portion.

When to use: Use to see how much actual loan-payoff progress a single payment makes. Useful for understanding why early mortgage payments barely move the balance, or how much principal an extra payment in year 5 would replace.

Calculator

Formula

P_p = \min\left(PMT,B_{p-1}(1+k/m)\right)-B_{p-1}k/m

Variables

Symbol	Name	Description	Unit
Principal	Principal Portion	Amount reducing the loan balance on payment p	$
PV	Original Loan	Original loan amount	$
PMT	Payment	Periodic payment amount	$
k	Annual Rate	Nominal annual interest rate as a decimal	%
m	Periods/Year	Number of payments per year (1 for annual, 12 for monthly)	integer
p	Payment Number	Which payment to compute (1 = first payment)	integer

Real-Life Examples

Example 1: First Mortgage Payment

$300,000 mortgage at 6% APR, monthly payments of $1,798.65 over 30 years. Principal portion of payment 1?

Given

PV = $300,000.00PMT = $1,798.65k = 6.0000%m = 12.00p = 1.00

Step-by-Step

1.Periodic rate = 0.06 / 12 = 0.005

2.For each payment: interest = prior balance × periodic rate; actual payment is capped at prior balance + interest

3.At payment 1: interest ≈ $1,500.00, principal ≈ $298.65, remaining balance ≈ $299,701.35

4.Principal ≈ $298.65

Result:$298.65

For these inputs, Principal Portion is $298.65 under the stated payment, compounding and accounting assumptions.

Example 2: Mid-Loan Payment

Same loan. What's the principal on payment 180 (year 15)?

Given

PV = $300,000.00PMT = $1,798.65k = 6.0000%m = 12.00p = 180.00

Step-by-Step

1.Periodic rate = 0.06 / 12 = 0.005

2.For each payment: interest = prior balance × periodic rate; actual payment is capped at prior balance + interest

3.At payment 180: interest ≈ $1,069.38, principal ≈ $729.27, remaining balance ≈ $213,146.99

4.Principal ≈ $729.27

Result:$729.27

For these inputs, Principal Portion is $729.27 under the stated payment, compounding and accounting assumptions.

Example 3: Final Payment

Same loan. Principal portion of the very last payment (p=360)?

Given

PV = $300,000.00PMT = $1,798.65k = 6.0000%m = 12.00p = 360.00

Step-by-Step

1.Periodic rate = 0.06 / 12 = 0.005

2.For each payment: interest = prior balance × periodic rate; actual payment is capped at prior balance + interest

3.At payment 360: interest ≈ $8.96, principal ≈ $1,789.69, remaining balance ≈ $1.58

4.Principal ≈ $1,789.69

Result:$1,789.69

For these inputs, Principal Portion is $1,789.69 under the stated payment, compounding and accounting assumptions.

Frequently Asked Questions

It depends on the rate, remaining term and payment. Compare the actual schedule rather than applying a universal crossover month.

The final payment is capped at the balance plus accrued interest. Payments after payoff contribute zero; a payment below interest produces negative principal and a growing balance.

Related Formulas

Interest Portion of Payment

Same family

Remaining Loan Balance

Present Value of an Annuity

Interest Portion of Payment Cumulative Interest Paid