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Loans & Amortization

Finly features a comprehensive debt and mortgage management engine with exact French amortization schedule mathematics, status tracking, and early repayment simulation.

Mathematical Formulation

Amortizing loans in Finly utilize the standard French fixed-rate annuity formula (constant total monthly installments with increasing principal and decreasing interest components):

1. Monthly Annuity Installment (\(M\))

\[M = P \times \frac{r(1 + r)^n}{(1 + r)^n - 1}\]

Where:

  • \(P\) = Initial borrowed principal capital
  • \(r\) = Periodic monthly interest rate: \(r = \frac{\text{Annual Interest Rate}}{100 \times 12}\)
  • \(n\) = Total loan duration in months (\(\text{duration\_months}\))

2. Borrower Insurance Installment (\(I_{\text{ins}}\))

For standard French loans where insurance is computed on the initial borrowed capital:

\[I_{\text{ins}} = P \times \frac{\text{Annual Insurance Rate}}{100 \times 12}\]

3. Total Monthly Payment (\(M_{\text{total}}\))

\[M_{\text{total}} = M + I_{\text{ins}}\]

Month-by-Month Amortization Schedule

For each payment period \(k\) from \(1\) to \(n\):

  1. Periodic Interest Component: $\(\text{Interest}_k = \text{Remaining Principal}_{k-1} \times r\)$

  2. Principal Amortization Component: $\(\text{Principal}_k = M - \text{Interest}_k\)$

  3. Remaining Capital: $\(\text{Remaining Principal}_k = \text{Remaining Principal}_{k-1} - \text{Principal}_k\)$

Live Status Computation

The engine calculates real-time metrics based on the loan's start_date and the current date:

  • Elapsed Payments (\(k\)): Number of monthly installments settled to date.
  • Remaining Payments (\(n - k\)): Months remaining until full loan maturity.
  • Amortized Capital: Cumulative sum of principal repaid.
  • Outstanding Capital: Current balance contributing to liability deductions in personal net worth.
  • Repayment Progress: \(\frac{\text{Amortized Capital}}{P} \times 100\%\).

Early Repayment Simulator

Finly provides an early repayment calculator allowing users to simulate lump-sum prepayments (e.g., 5,000 EUR or 20,000 EUR):

flowchart TD
    Prepay["Prepayment Amount (e.g., 10,000 EUR)"] --> IRA["Compute French Legal IRA Penalty"]
    IRA --> Choice{"Simulation Strategy"}

    Choice -- Strategy A --> Duration["Shorten Loan Duration"]
    Choice -- Strategy B --> Payment["Reduce Monthly Installment"]

    Duration --> DurOut["Keeps installment constant<br>Shortens maturity<br>Maximizes interest savings"]
    Payment --> PayOut["Keeps maturity date constant<br>Reduces monthly burden<br>Improves monthly cash flow"]

Under Article L313-47 of the French Consumer Code, early repayment penalties for residential property loans cannot exceed:

\[\text{IRA} = \min\left(\text{Repayment Amount} \times 3\%,\; \text{Repayment Amount} \times \frac{\text{Annual Interest Rate}}{100} \times \frac{6}{12}\right)\]

Finly automatically applies this legal cap when computing simulated net interest savings.