INSTALLMENT OF A CREDIT

 

Have you ever wondered? Because those people who acquire a bank loan and have been paying in a timely manner for 3 or 4 years, the total debt seems not to decrease significantly? This is due to the fact that an important part of the total payment that is made is used to pay interest that the bank charges for having granted the loan and what is left is assigned to settle the initial debt or unpaid balance.

But what is the repayment of a loan?

When a loan is requested and it is intended to pay in installments, each of these credits is composed of interest and part of capital. The action to cancel part of the capital in each one of the payments is called amortization of the credit.

The breakdown of payments can be clearly seen in an amortization table. This table is calculated by the banks according to the characteristics of the credit (amount, term and interest rate).

It is important to mention that there are different ways to amortize a loan and these depend mainly on the way in which the amount of capital is reduced; However, before explaining some of the amortization methods, it is important to review the following topics: geometric progressions, annuities and the present value of an annuity; amortization.

Geometric progressions

If ayr are fixed numbers not equal to zero, then the infinite list of numbers a, ar, ar 2 , ar 3 , ar 4 ,. . . . it is called a geometric sequence or geometric progression. For example, if a = 5 and r = 2, we have the sequence: 5, (5) (2), (5) (2) 2 , (5) (2) 3 , (5) (2) 4 ,. . . . or 5, 10, 20, 40, 80

Example $ 100.00 is deposited into an account that pays 10% interest compounded annually. How much is in the account at the beginning of each of the first five years?

According to the formula for compound interest (with P = 100 and i = 0.01), the value of the account at the beginning of each of the first 5 years is given by the first five terms of the geometric progression with a = 100 yr = 1.1. The first 5 terms are:

100, 100 (1.1), 100 (1.1) 2 , 100 (1.1) 3 , 100 (1.1) 4

So the value of the account at the beginning of each of the five years is:

$ 100.00, $ 110.00, $ 121.00, $ 133.10, $ 146.41

Annuities

An annuity is a succession of equal payments that are made in equal periods and this may be ordinary, anticipated or deferred.

Ordinary annuities: Annuities begin to be paid from period 1.

Example. Suppose that $ 1,500.00 is deposited at the end of the year during the following years in an amount that pays 8% per year compounded annually.

1500 (1.08) 5

The 5 is used as an exponent, instead of the 6, since the money is deposited at the end of the first year and earns interest for only 5 years.

1500 (1.08) 5 + 1500 (1.08) 4 + 1500 (1.08) 3 + 1500 (1.08) 2 + 1500 (1.08) + 1500

$ 2,203.99; $ 2,040.73; $ 1,889.57; $ 1,749.60; $ 1,620.00; $ 1,500.00

$ 11,003.89

To perform the calculation easily, the following formula can be applied:

Advance Annuities : Annuities begin to be paid from period 0.

To find the future value of an anticipated annuity, each payment is treated as if it were done at the end of the preceding period. No payment is made at the end of each period, so to compensate for this, the amount of a payment is subtracted.

Considering the previous problem and applying the following formula:

Is obtained:

Present value of an annuity

The present value of an annuity is the sum of the present values of the different payments, each one discounted at the beginning of the term.

It is important to remember the way in which the present value of compound interest is calculated.

Capitalize: add interest 

Update: Discount, remove interest 1 

Example. Find the current value of an ordinary annuity of $ 1,000.00 per month, for 4 months to 5% per month.

To perform the calculation easily, the following formula can be applied:

As previously mentioned, and taking up the main theme, there are various ways to amortize a loan and these depend mainly on the way in which the amount of capital is reduced. Here are two ways of repaying a loan: fixed and declining rate.

one). Fixed fee : In this method, as the name indicates, all fees or payments must be equal. To calculate the quota, the formula of the present value of an annuity (VPA) reviewed in the previous section is used.

For a better understanding of the fixed fee method, a real amortization table of a bank loan will be constructed; Therefore, it is important to mention that when paying off a loan, and in accordance with Mexican tax legislation, you must pay 16% of the Value Added Tax (VAT) calculated on the interest that will be paid for the credit contracted.

Example. Build a table of amortization of a bank loan for an amount of $ 15,912.12 to a term of 60 months and a rate of 23.72% per year, considering a VAT of 16%.

When you clear R, you get that the amount of the fixed payment is $ 490.79. The corresponding amortization table is shown below:

Amortization table by the fixed installment method
Payment Insolute Capital Capital payment Subscription Interest VAT Fixed payment
one $ 15,912.12 $ 125.94 $ 314.53 $ 50.32 $ 490.79
two $ 15,786.18 $ 128.83 $ 312.04 $ 49.93 $ 490.79
3 $ 15,657.35 $ 131.78 $ 309.49 $ 49.52 $ 490.79
4 $ 15,525.57 $ 134.80 $ 306.89 $ 49.10 $ 490.79
5 $ 15,390.77 $ 137.89 $ 304.22 $ 48.68 $ 490.79
6 $ 15,252.88 $ 141.06 $ 301.50 $ 48.24 $ 490.79
7 $ 15,111.82 $ 144.29 $ 298.71 $ 47.79 $ 490.79
8 $ 14,967.53 $ 147.60 $ 295.86 $ 47.34 $ 490.79
9 $ 14,819.93 $ 150.98 $ 292.94 $ 46.87 $ 490.79
10 $ 14,668.95 $ 154.44 $ 289.96 $ 46.39 $ 490.79
eleven $ 14,514.51 $ 157.99 $ 286.90 $ 45.90 $ 490.79
12 $ 14,356.52 $ 161.61 $ 283.78 $ 45.40 $ 490.79
13 $ 14,194.91 $ 165.31 $ 280.59 $ 44.89 $ 490.79
14 $ 14,029.60 $ 169.10 $ 277.32 $ 44.37 $ 490.79
fifteen $ 13,860.50 $ 172.98 $ 273.98 $ 43.84 $ 490.79
16 $ 13,687.52 $ 176.95 $ 270.56 $ 43.29 $ 490.79
17 $ 13,510.57 $ 181.01 $ 267.06 $ 42.73 $ 490.79
18 $ 13,329.56 $ 185.16 $ 263.48 $ 42.16 $ 490.79
19 $ 13,144.41 $ 189.40 $ 259.82 $ 41.57 $ 490.79
twenty $ 12,955.01 $ 193.74 $ 256.08 $ 40.97 $ 490.79
twenty-one $ 12,761.26 $ 198.19 $ 252.25 $ 40.36 $ 490.79
22 $ 12,563.08 $ 202.73 $ 248.33 $ 39.73 $ 490.79
2. 3 $ 12,360.35 $ 207.38 $ 244.32 $ 39.09 $ 490.79
24 $ 12,152.97 $ 212.13 $ 240.22 $ 38.44 $ 490.79
25 $ 11,940.83 $ 217.00 $ 236.03 $ 37.76 $ 490.79
26 $ 11,723.83 $ 221.97 $ 231.74 $ 37.08 $ 490.79
27 $ 11,501.86 $ 227.06 $ 227.35 $ 36.38 $ 490.79
28 $ 11,274.80 $ 232.27 $ 222.87 $ 35.66 $ 490.79
29 $ 11,042.53 $ 237.60 $ 218.27 $ 34.92 $ 490.79
30 $ 10,804.93 $ 243.04 $ 213.58 $ 34.17 $ 490.79
31 $ 10,561.89 $ 248.62 $ 208.77 $ 33.40 $ 490.79
32 $ 10,313.27 $ 254.32 $ 203.86 $ 32.62 $ 490.79
33 $ 10,058.95 $ 260.15 $ 198.83 $ 31.81 $ 490.79
3. 4 $ 9,798.81 $ 266.11 $ 193.69 $ 30.99 $ 490.79
35 $ 9,532.69 $ 272.22 $ 188.43 $ 30.15 $ 490.79
36 $ 9,260.48 $ 278.46 $ 183.05 $ 29.29 $ 490.79
37 $ 8,982.02 $ 284.84 $ 177.54 $ 28.41 $ 490.79
38 $ 8,697.18 $ 291.37 $ 171.91 $ 27.51 $ 490.79
39 $ 8,405.81 $ 298.05 $ 166.15 $ 26.58 $ 490.79
40 $ 8,107.75 $ 304.89 $ 160.26 $ 25.64 $ 490.79
41 $ 7,802.86 $ 311.88 $ 154.24 $ 24.68 $ 490.79
42 $ 7,490.99 $ 319.03 $ 148.07 $ 23.69 $ 490.79
43 $ 7,171.96 $ 326.35 $ 141.77 $ 22.68 $ 490.79
44 $ 6,845.61 $ 333.83 $ 135.31 $ 21.65 $ 490.79
Four. Five $ 6,511.78 $ 341.48 $ 128.72 $ 20.59 $ 490.79
46 $ 6,170.30 $ 349.31 $ 121.97 $ 19.51 $ 490.79
47 $ 5,820.99 $ 357.32 $ 115.06 $ 18.41 $ 490.79
48 $ 5,463.66 $ 365.52 $ 108.00 $ 17.28 $ 490.79
49 $ 5,098.15 $ 373.90 $ 100.77 $ 16.12 $ 490.79
fifty $ 4,724.25 $ 382.47 $ 93.38 $ 14.94 $ 490.79
51 $ 4,341.78 $ 391.24 $ 85.82 $ 13.73 $ 490.79
52 $ 3,950.54 $ 400.21 $ 78.09 $ 12.49 $ 490.79
53 $ 3,550.33 $ 409.39 $ 70.18 $ 11.23 $ 490.79
54 $ 3,140.95 $ 418.77 $ 62.09 $ 9.93 $ 490.79
55 $ 2,722.17 $ 428.38 $ 53.81 $ 8.61 $ 490.79
56 $ 2,293.80 $ 438.20 $ 45.34 $ 7.25 $ 490.79
57 $ 1,855.60 $ 448.25 $ 36.68 $ 5.87 $ 490.79
58 $ 1,407.35 $ 458.52 $ 27.82 $ 4.45 $ 490.79
59 $ 948.83 $ 469.04 $ 18.76 $ 3.00 $ 490.79
60 $ 479.79 $ 479.79 $ 9.48 $ 1.52 $ 490.79

To start the construction of the table, once you have the amount of the fixed payment, the interest payment is first calculated and for this the unpaid capital is multiplied by 0.01976 (15,912.12 X 0.01976 = 314.53). 0.01976 is the result of dividing 23.72% between twelve months. Subsequently, the interest payment is multiplied by 16% to obtain VAT (314.53 X 0.16 = 50.32), and finally, the fixed payment is subtracted from the sum of the interest payment plus VAT to obtain the capital payment (490.79 – 364.85 = 125.94). For the next period the same procedure is performed; but the initial insolute capital is no longer used, but the capital payment is subtracted to obtain the unpaid capital to be used in the following period (15,912.12 – 125.94 = 15,786.18).

But where do you get 0.0229? You get 16% of the rate of 23.72% and the result obtained is added to this rate (23.72 X 1.16 = 27.5252) and the final result is divided by twelve to convert the annual rate into monthly (27.5252 / 12 = 2.29).

It is important to mention that the fixed fee method is the most used by banks in Mexico, so it was decided to construct the amortization table in a real way. Through this exercise, and as mentioned at the beginning, it can be observed that part of the total payment that is made is used to pay interest and what is left is assigned to settle the initial debt or unpaid balance.

The process of building an amortization table corresponding to a mortgage loan or a credit for the purchase of a car is similar to the one developed in this case.

two). Decreasing share : In this method the depreciation is the same for all periods, the depreciation must be calculated first.

Formula to calculate the amortization

Example. Build a table of amortization of a debt of $ 1000.00 that must be repaid in 4 months at an effective rate of 5% per month.

Amortization table by the declining installment method
Payment Insolute capital Capital payment Subscription Interest Fixed payment
one $ 1,000.00 $ 250.00 $ 50.00 $ 300.00
two $ 750.00 $ 250.00 $ 37.50 $ 287.50
3 $ 500.00 $ 250.00 $ 25.00 $ 275.00
4 $ 250.00 $ 250.00 $ 12.50 $ 262.50

 

All information on mortgage insurance rates

This online borrower insurance comparator gives access to all offers available on the market.

What is a mortgage insurance rate?

When we come to find the house of our dreams, are we still trying to do everything to get it? If we do not want to touch the few savings we have, it becomes extremely difficult. So, to avoid missing out on this opportunity, we must seek the quickest solution to obtain the necessary funding. 

What is a mortgage insurance rate?

Faced with this, people often tend to borrow from their bank. It is indeed a brilliant idea to acquire credit in due time. But when we ask for this kind of loan, the bank claims in return the mortgage insurance rates . The applied rate is, in a way, the interest that the banks draw.

How are property insurance rates defined?

Before jumping directly to a signature about the loan, it is undeniable to bypass the subject of the mortgage rate. The latter is therefore the result of calculations made according to several points. It varies according to each bank. Thus, we are not obliged to apply for a credit to the bank in which we are registered. Playing the competition is important and perhaps borrowing from an organization other than our current bank will earn us more benefits.

In addition, the rate of insurance varies according to the situation of each person. For more details, one must take into account the age factor of the borrower and also his health. It is sort of a risk assessment of insurance. Several questions are asked to the borrower to know his state of health. As a result, the more people are prone to illness, the higher the cost of the insurance rate.

Added to this, the rate is defined according to the credit we want to borrow. It is quite right that if the amount you ask for is high, the insurance rate goes up. And it is during the first 12 months that the reimbursement has a high price. And after this year, the capital remaining due decreases during the last years of repayment.

And finally, in general, everything will depend on each organization in which we apply for credits. Each organization offers a multitude of credit offers. However, we will lose a lot of time if we move to collect offers from the lenders. With borrower.io, the comparison of various quotes on the market becomes extremely easy.

shutterstock 11705748101 960x667 

 

Personal loan online, what to remember

You plan to grant a personal loan, you still hesitate where you will go. However, a friend has advised you on personal loan online, but you are puzzled. Here, discover the benefits of this financing solution to help you make a decision.

 

Who offers the personal loan online

For some time online banks have been on the rise to compete with conventional credit institutions that offer exorbitant interest rates. The benefits are not lacking to seduce new customers daily.

What benefits with personal loan online

What benefits with personal loan online

With a personal loan online , the borrower is not obliged to explain the use of money to borrow. So, he has total freedom of what he will do with the amount he will get:

travel, buy a new car, change your wardrobe, do some renovation work in your home or others. Many people also take out a personal loan online to reimburse other credits.

Unlike other loans, the personal loan online is very flexible. It is possible to ask for sums ranging from 1500 euros to 21500 euros, depending on the needs of the borrower. But what about refunds? Depending on the case and depending on the amounts requested, it varies between 12 and 60 months. All this, you will get it by staying at home. If the agreement is signed, your account will be debited in 48 hours.

Personal loan online

Who can grant the personal loan online?

The personal loan online is accessible to everyone and requires very few guarantees. Be aware that in other lending institutions, some people can not apply for a large personal loan. In short, it is a very beneficial and simple solution. It will be easy for you to know exactly how much you will pay at the end of each month and at what pace. With online banks, finished the bad surprises on his account.

Before you start a personal loan online

Of course, the personal loan online is very attractive, but be sure to determine your need for money to avoid over-indebtedness. You will also need to properly assess your repayment capacity taking into account your fixed and occasional expenses. Do not forget to compare the offers of personal loan banks online. To do this, use a simulator because the interest rate varies depending on the amount borrowed and the repayment period.

Financing an onshore wind farm project

WFW advises lenders on the project financing of the onshore wind farm “Malaspina” in Argentina

(WK-intern) – International commercial law firm Watson Farley & Williams (“WFW”) has acquired KfW IPEX-Bank GmbH, Kreditanstalt für Wiederaufbau (KfW) and Nederlandse Financierings-Maatschappij voor Ontwikkelingslanden NV (FMO) at USD 104 million. Advised on the financing of the onshore wind farm project Malaspina.

The project is located in the province of Chubut in the south of Argentina

The loan documentation was signed in December 2018. The financing was completed in January 2019 and is partially secured by an ECA guarantee from the German export credit agency Euler Hermes. The wind park is indirectly owned by the French company Total Eren SA, a leading independent power producer (IPP) for renewable energy. Total Eren also developed the project himself. Upon completion, it will provide a total output of 50.4 MW generated by 14 Senvion wind power generators, each with 3.6 MW.

Senvion wind turbines / Photo: HB

Founded in 2012, Total Eren owns more than 1,700 MW of wind, solar and hydropower plants that are in operation or under construction worldwide. Together with local developers, Total Eren is currently developing numerous energy projects in regions with a growing need for renewable energy, such as in Latin America, Africa and the Asia-Pacific region

The WFW advisory team was headed by the Hamburg partner dr. Stefan Kilgus (Banking & Finance). He was assisted by managing associate dr. Pascal Unger and associate Jens Leu (both Banking & Finance Hamburg). In addition, Corporate / Energy Partners advised Stefan Hoffmann (Hamburg) on project-related aspects of the transaction and Finance Partner Philippe Wolanski (Paris) on French law issues. WFW worked closely with Argentine law firm Bruchou, Fernández Madero & Lombardi on aspects under Argentine law.

The leading partner Stefan Kilgus comments: “We are very pleased to have advised the lenders on a third non-recourse project financing project in Argentina. We are particularly pleased that we were again allowed to work on a Total Eren project. This mandate underscores the significant role and capacity of WFW in international energy projects, particularly in Latin America and Argentina. “

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