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Personal Loan Payment and Amortization Formulas

Review personal loan formulas for fixed monthly payment, origination fees, cash proceeds, amortization, extra principal, payoff time, and total interest.

How do the Personal Loan Calculator formulas work?

This formula page defines the variables used by the Personal Loan Calculator, shows how those values are combined, and explains the order of operations behind the result. Use the worked steps to verify an estimate, compare scenarios, and understand which assumptions or rounding rules can affect the displayed answer.

Formula Overview

The calculator determines the origination fee and financed principal first. It then solves the fixed monthly payment and generates two cents-posted schedules: the standard contract schedule and an accelerated schedule with the entered extra monthly principal.

This sequence keeps the fee treatment explicit. A deducted fee changes cash proceeds but not principal. A financed fee increases principal, payment, and interest.

Variable Definitions

SymbolMeaningUnit or convention
ARequested loan amountCurrency
fOrigination fee ratePercentage
FOrigination fee amountCurrency
PFinanced principalCurrency
NNet cash proceedsCurrency
rAnnual fixed note ratePercentage
iMonthly rater / 1,200
nScheduled payment countYears x 12 + months
MScheduled monthly paymentCurrency per month
EExtra monthly principalCurrency per month
BtBalance after payment tCurrency

Fixed Monthly Payment

For a positive note rate, the standard level-payment formula is:

M=Pi(1+i)n(1+i)n−1M=P\frac{i(1+i)^n}{(1+i)^n-1}

The calculator converts the entered annual percentage to a monthly decimal rate with i = r / 1,200. When the rate is zero, it uses:

M=PnM=\frac{P}{n}

The scheduled payment is rounded to cents before the amortization schedule is built.

Monthly Amortization

For each period, interest is calculated from the prior cents-posted balance. Scheduled principal is the payment left after interest:

It=round(Bt−1i,2)I_t=round(B_{t-1}i,2)
Qt=min⁡(Bt−1,round(M−It,2))Q_t=\min\left(B_{t-1},round(M-I_t,2)\right)
Bt=round(Bt−1−Qt,2)B_t=round(B_{t-1}-Q_t,2)

The final principal posting is capped at the remaining balance. Total interest equals the sum of monthly interest rows, and the final balance reconciles to zero.

Extra Monthly Principal

The accelerated schedule adds the entered extra amount to the planned payment:

Mplanned=round(M+E,2)M_{planned}=round(M+E,2)
Qtextra=min⁡(Bt−1,round(Mplanned−It,2))Q_t^{extra}=\min\left(B_{t-1},round(M_{planned}-I_t,2)\right)
Interest saved=∑Itstandard−∑ItextraInterest\ saved=\sum I_t^{standard}-\sum I_t^{extra}
Months saved=nstandard−nextraMonths\ saved=n_{standard}-n_{extra}

The last payment may be smaller because principal cannot exceed the remaining balance.

Origination Fee, Amount Financed, and Proceeds

F=round(Af100,2)F=round\left(A\frac{f}{100},2\right)
P=A+Fwhen the fee is financedP=A+F\quad\text{when the fee is financed}
N=A−Fwhen the fee is deductedN=A-F\quad\text{when the fee is deducted}

When the fee is deducted, P = A. When the fee is financed, N = A. The displayed fee-inclusive borrowing cost is total interest plus the origination fee; it is not a lender-disclosed APR calculation.

Worked Calculation

For a $25,000.00 request, 10% fixed note rate, 36 months, and a 2% fee deducted from proceeds:

  1. Fee: $25,000.00 x 2% = $500.00.
  2. Financed principal: $25,000.00.
  3. Net proceeds: $25,000.00 - $500.00 = $24,500.00.
  4. Monthly rate: 10 / 1,200 = 0.0083333333.
  5. The fixed-payment formula produces $806.68.
  6. First-month interest: $25,000.00 x 0.0083333333 = $208.33.
  7. First-month principal: $806.68 - $208.33 = $598.35.
  8. The 36-row schedule produces $4,040.50 of interest and $4,540.50 of interest plus fee.

Assumptions and Exclusions

  • The note rate is fixed and interest is calculated monthly.
  • Payments are made on schedule and amounts are posted to cents.
  • The origination fee is either fully deducted or fully financed according to the selected option.
  • Extra payments are credited directly to principal without a prepayment charge.
  • The model excludes variable rates, late fees, optional insurance, daily-interest conventions, skipped payments, refinancing, and lender-specific APR calculations.
  • The result is not an approval decision or credit offer.

Formula FAQ

Why does financing the fee increase interest?

The fee becomes part of principal, so monthly interest is calculated on a larger balance. For a useful Personal Loan Calculator formula result, enter realistic values, compare relevant scenarios, check the calculation details, and review the definitions, assumptions, and limitations before using the estimate for an important decision.

Why can total payments differ slightly from payment times months?

The schedule posts interest and principal to cents and adjusts the final payment to the exact remaining balance. For a useful Personal Loan Calculator formula result, use realistic inputs, compare relevant scenarios, and review the stated assumptions before making a decision.

Why does extra principal save interest?

It reduces the balance used by later interest calculations. Earlier reductions affect more future periods. For a useful Personal Loan Calculator formula result, enter realistic values, compare relevant scenarios, check the calculation details, and review the definitions, assumptions, and limitations before using the estimate for an important decision.

Does the calculator compute legal APR?

No. It models note-rate amortization and an entered origination fee. Use the lender's disclosure for APR. For a useful Personal Loan Calculator formula result, enter realistic values, compare relevant scenarios, check the calculation details, and review the definitions, assumptions, and limitations before using the estimate for an important decision.

References

Use the worked personal loan examples to reproduce these formulas with complete scenarios.

Use the Personal Loan Calculator