How to calculate the quota of a loan

The quota of a loan is the amount that is due periodically to pay after to acquire one, with the purpose of to be giving back part of this one and, simultaneously, to be paying the interests that have been received to acquire it.

Besides the amount of the loan, the interest rate and the granted term, to determine the quota to pay the method or system of amortization that uses the bank or financial organization are due to take into account that grant the credit; which basically use two methods: the German method and the French method.

We see next each of them:

1. German method

The German method is very nowadays not used; in this method the quotas are decreasing, that is to say, at the outset high quotas are pleased, but soon they are falling.

In order to understand this method, we see an example:

We suppose that we have acquired a loan of US$1 000, to a monthly interest rate of of 4%, by a period of 5 months.

In order to find the quota using the German method, first of all, because in this method the amortizations are constant, we found the amortizations dividing the loan (1000) between the number of periods (5), and then, we found the balances that go been of the debt when being deducing the amortizations to him:

n	Balance	Amortization	Interest	Quota
0	1000
1	800	200
2	90	200
3	400	200
4	200	200
5	0	200
Total		1000

Then, to determine the interests to pay, for the first period, we applied the interest rate (4%) on the loan (1000), and soon on the balances of the debt that are being:

n	Balance	Amortization	Interest	Quota
0	1000
1	800	200	40
2	90	200	32
3	400	200	24
4	200	200	16
5	0	200	8
Total		1000	120

And, finally, to find the quotas to pay, we added the amortizations plus the interests:

n	Balance	Amortization	Interest	Quota
0	1000
1	800	200	40	240
2	90	200	32	232
3	400	200	24	224
4	200	200	16	216
5	0	200	8	208
Total		1000	120	1120

In the first period (first month), we will pay a quota of US$240, in the second month we will pay a quota of US$232, and so on.

2. French method

The French method is used; in this method the quotas are fixed, that is to say, all the periods the same quota is pleased.

In order to find the quota using the French method, we used the following formula:

R = P [(i (1 + i) n)/((1 + i) n - 1)]

Where:

R = rent (quota)

P = main (acquired loan)

i = interest rate

n = number of periods

We see an example:

We suppose that we have acquired a loan of US$ 1 000, to a monthly interest rate of of 4%, by a period of 5 months (similar to the previous example).

Applying the formula:

R = P [(i (1 + i) ⁿ)/((1 + i) ⁿ - 1)]

R = 1000 [(0,04 (1 + 0,04) ⁵)/((1 + 0,04) ⁵ - 1)]

R = 224.63

It gives a quota us of US$224.63:

n	Quota	Interest	Amortization	Balance
0				1000
1	224.63
2	224.63
3	224.63
4	224.63
5	224.63
Total	1123.14

In order to find the interests, for the first period, we applied the interest rate (4%) on the loan, and soon on the balances that are being; in order to find the amortizations we reduced the interests to the quotas; and to find the balances of the debt we reduced the amortizations to the previous balances:

n	Quota	Interest	Amortization	Balance
0				1000
1	224.63	40	184.63	815.37
2	224.63	33	192.01	623.36
3	224.63	25	199.69	423.67
4	224.63	17	207.68	215.99
5	224.63	9	215.99	0
Total	1123.14	123.14	1000

Final notes

In order to find the quota using the French method, before to use the described formula, previously simplest it is to use Excel. For it we must use the formula “payment”, where when using it we must indicate:

• Rate: interest rate
• Nper: number of periods
• It goes: present value (value of the loan)

Another important note that to stand out it is that before carrying out the calculation of a quota, we must as much make sure that the interest rate as the period of the payments, they agree in the same period of time; for example, if it is an annual rate, the payments also would have to be realized annually; in case of not being thus, we must turn the period of the rate to the same period of time in which the payments are programmed.

For it, we used the following formula:

Teq = [(1 + i) 1/n - 1] x 100

Where:

Teq = equivalent rate

n = number of periods that the rate includes/understands that is wanted to find with respect to the number of periods that the original rate includes/understands.

Most common it is than an annual rate is indicated, and that the payments are monthly, reason why in that case, we must find a monthly rate equivalent to the annual one; for example, if one is an annual effective rate (TEA) of 38%, to find the effective rate monthly (TEM) equivalent, we applied the formula:

Teq = [(1 + i) ^1/n - 1] x 100

Teq = [(1 + 0,38) ^1/12 - 1] x 100

Teq = 2,72%

What it gives an equivalent rate us of 2,72%, that is to say, the TEA of 38% is equivalent to a TEM of 2,72%.