__WHAT IS THE FRENCH AMORTIZATION METHOD OF A BANKING LOAN__

In the following post it will be explained **how to solve a banking loan following the French amortization method that is widely used in the financial industry**.

The main characteristic of this methodology is that the installments or payments are always a fixed amount (“C”) comprised of interests (“I”) and amount amortized from the principal or amount borrowed (“K”).

A banking loan amortized by the French method will always have the following 5 columns:

- “K”: Outstanding debt or principal amount (money that the company owes).
- “C”: Fixed installment, comprised of interest and amount amortized.
- “I”: Interests paid in the period and defined by “Kd”.
- “A”: Amount amortized or paid back from the principal amount borrowed.
- Cash-flow generated by the loan.

The financial condition that must be met in any banking loan is that the present value of the banking debt cash-flows must be equal than the money borrowed in t=0, at the interest rate of the loan, defined as “Kd” or cost of debt. Under this financial equation, the fixed payment or installment formula is as follows, where the incognita “C” must be obtained:

**Amount borrowed (K) = Fixed installment (C) * [(1-(1+interest)^(-time)] / interest**

It is very important to note, that in the formula, the interest and time must be in the same time units. For example, if the payments are undertaken yearly, the installments “C” are yearly and the interest rate Kd must be a nominal yearly interest. The time period should be years. If the installments are monthly, the interest Kd must be a monthly nominal rate and the time must be in months. For example, if Kd=12% yearly and time t=5 years, but the payments are monthly, the interest rate to be used in the formula is 12%/12 months=1% and the time period=5*12=60 months.

Once the “C” fixed installment is calculated, we must calculate the interests paid in the period “t” (“I”). The outstanding amount or debt at the beginning of the period “t-1” (“D”)*interest yield “Kd” will produce an output of the interests paid in that period “t”. “C”-“I” will allow to calculate the amount amortized “A” in that period of time “t”. Then, the level of outstanding debt in “t” will be level of outstanding debt in “t-1” minus the amount amortized in “t”.

In order to validate that the banking loan has been correctly solved, the sum of all the amounts amortized must be the amount of money borrowed from the bank “K”. Additionally, the level of outstanding debt the last year must be zero. If these two conditions are not met, the banking loan table is wrong, and calculations must be revised.

Please find below an example of a banking loan table following the french amortization table and with the following conditions:

- “K”=Amount borrowed €7,729,890
- Frequency of payments: Semi-annual.
- Yearly nominal interest (“Kd”)=5%. Semi-annual nominal interest (5%/2=2,5%)
- Time: 3 years (3*2=6 semesters)

The we proceed to solve the problem:

- Applying the formula, the semi-annual fixed payments or installments, “C”=€1,403,361
- Semi-annual interests paid in the first semester: 2,5%*€7,729,890=€193,247
- Amortized amount in the first semester t=1: C-I=€1,403,361-€193,247=€1,210,114
- Outstanding debt level (“D”) at the end of the first semester (t=1)=€6,519,776
- Please note that the cash-flow calculation analyzes de cash inflows and outlays from the company perspective.
- If we repeat this calculation for each semester, we obtain the following table.
- Please note that the total amount of payments would be: 6*€1,403,361=€8,420,168 (€7,729,890 amount borrowed+€690,278 interests paid).

**A BANKING LOAN TABLE (FRENCH AMORTIZATION METHOD)**