# Assigned Loan

An **assigned loan, or assigned credit,** is a category of consumer credit granted in France by a bank or financial institutionintended to finance the purchase of a good or service (usually domestic or professional equipment). The main characteristic of the loans affected is that the obligations towards the bank arise only from the delivery of the good. If the purchase does not finally take place or the property has not been delivered, the credit is automatically canceled. On the other hand, the destination of the money lent can not be changed and the funds can not be used for anything other than the act. He is opposed to other consumer credits that are intended to cover a cash flow requirement or that do not have a specific purpose such as revolving credit or personal loan .

## Characteristics

Often the property concerned is taken as collateral (pledge on automobile for example), and the duration of the loan is less than the foreseeable lifetime of the good.

These credits are often offered at the point of sale of the good or service. The financing granted is directly paid into the hands of the seller, without going through the lender’s account (unlike a traditional personal loan).

Note also another important feature related (in French law) to the applicable rate and more specifically to the rate of wear . The rate of wear not to exceed is different from that of a conventional personal loan. This type of loan called by the Bank of France “installment purchase financing” will admit a Global Effective Actuarial Rate (GTAR) more than twice higher than that of a traditional personal loan, for an individual, not assigned to the purchase of a good or service. ^{1}

This type of loan, which is often granted with greater ease than a personal loan , entails a greater risk for the lender; the rate will therefore be higher, which allows the regulation, since it appears on the offer including the specific description of the good or service purchased, as well as the seller’s contact information.

In return, the loan is incidental to the sale, which means in plain language that if a dispute arises between the seller and the buyer / borrower and in the end the sale is canceled, the loan will be canceled (which is not the case for a personal loan whose funds can be freely used by the borrower). The seller will have to return the funds received from the lender (the bank or the financial institution), the lender will repay the installments paid by the borrower.

## Calculation of the amount of monthly installments in fixed rate

*The following formulas apply to any repayment loans to fixed rate* .

notations:

- S0: the sum borrowed,
- M: the amount of the fixed rate monthly payment,
- Ta: the annual interest rate,
- n: the duration of the loan in months.

We start by calculating Tm the monthly interest rate:

{\ displaystyle T_ {m} = exp ({{1} \ over {12}} ln (1 + T_ {a} / 100)) – 1}

or {\ displaystyle ln (x),} denotes the logarithm of x (ln key on a calculator) and {\ displaystyle exp (x)} the exponential function (key {\ displaystyle e ^ {x}} )

The amount of the monthly payments is then given by

{\ displaystyle M = S_ {0} {{T_ {m} (1 + T_ {m}) ^ {n}} \ over {(1 + T_ {m}) ^ {n} -1}}}

The cost of credit (C) is then

{\ displaystyle C = nM-S_ {0}}

For example, for 300,000 euros, borrowed at a teg of 3.5% over 20 years (n = 20 * 12 = 240 months), the monthly interest rate is

{\ displaystyle T_ {m} = exp ({{1} \ over {12}} ln (1 + 3.5 / 100)) – 1 = 0.00287089 …..}

and the amount of monthly payments

{\ displaystyle M = S_ {0} {{T_ {m} (1 + T_ {m}) ^ {n}} \ over {(1 + T_ {m}) ^ {n} -1}} = 300000 { {0.00287089 (1 + 0.00287089) ^ {240}} \ over {(1 + 0.00287089) ^ {240} -1}} = 1731.42 …}

The cost of credit is

{\ displaystyle nM-S {0} = 240 * 1731.42-300000 = 115540.80euros}

**Calculation of the loanable amount in fixed rate**

Ratings: S0 the loanable amount, M the fixed rate monthly payment, Ta the annual interest rate, n the loan term in months.

We start by calculating Tm the monthly interest rate:

{\ displaystyle T_ {m} = exp ({{1} \ over {12}} ln (1 + T_ {a} / 100)) – 1}

or {\ displaystyle ln (x),} denotes the logarithm of x (ln key on a calculator) and {\ displaystyle exp (x)} the exponential function (key {\ displaystyle e ^ {x}} )

The amount of the loanable amount is then given by

{\ displaystyle S_ {0} = M {{((1 + T_ {m}) ^ {n} -1)} \ over {T_ {m} (1 + T_ {m}) ^ {n}}}

For example, to calculate the loanable amount over 15 years (n = 180 months), with a teg of 3.80%, and monthly payments of 1 000 euros , we start by calculating the monthly interest rate.

{\ displaystyle T_ {m} = exp ({{1} \ over {12}} ln (1 + 3.80 / 100)) – 1 = 0.00311281 ……}

and the amount of the loan amount is then

{\ displaystyle S_ {0} = M {{((1 + T_ {m}) ^ {n} -1)} \ over {T_ {m} (1 + T_ {m}) ^ {n}}} = 1000 {{((1 + 0.00311281) ^ {180} -1)} \ over {0.00311281 (1 + 0.00311281) ^ {180}}} = 137646.82euros}

## References

- ↑ See in this regard the wear rate applicable at the time (updated quarterly) [ archive ]