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Calculate a borrowing base formulas

In this part of the blog, I will try to simplify understanding of financial mathematics applied to various calculations of a loan or a loan. I'm not going to prove the formulas that I'll explain here but I will concentrate more on their meaning and usefulness in practice every day to prevent this from being an abstract mathematical or private practice almost every direction.

In the following formulas, you have the essentials of mathematical finance , you can deduct all other forms with some simple mathematical keys.

Vo Present value of future value discounted at Vn n periods rate i

Value Vn acquired by capital Vo n placed for periods at a rate i



Update / Capitalization :



The first formula represents the present value V 0 ( updating) a future value V n over n periods discounted at a rate i. From this formula we deduce the future value or acquired V n ( capitalization) versus V 0 capital invested for n periods at a rate i.


Some practical examples of these formulas:

1. How do I place today at 8% for 10 000 Euro in 3 years?


2. I want to buy a car in 5 years at a price of 50,000 Euro, the bank offered me an interest rate of 12%. How do I place a monthly basis so I can have that exact amount in 5 years?

To better answer this question, we must learn to correctly translate the data on a timeline and ask the same question but as a diagram.

With V n = 50 000 Euro and n = 60

So the question rephrased in this scheme is how much I have to place monthly now that I have, thanks to these products investments after the fifth year, ie in 60 months, amounting to 50 000 Euro?

He must know that the rate proposed by the bank is an annual rate it is necessary to convert to monthly rate. To do this we must distinguish between a proportional rate and an equivalent rate. Monthly rate proportional

= annual rate / 12 months (banks used incorrectly because this rate is equivalent to the rate of interest but not simple compounds. Indeed, the placement of a Euro in simple interest monthly at i will give at the end of the year an amount of interest 12i. On the other hand, the product of that interest placement for a year at the rate r would give an amount of interest equal r. So, assuming the equivalence of these two amounts of interest we get the formula for the proportional rate)

rate equivalent: it is in fact the monthly rate that would produce the same result as the annual rate in the case of investing the same amount.

Just for information, the level of bank loans and mortgages especially, we use the proportional rate and not the equivalent of what benefits most banks since the proportional rate (1 / 12 = 1 % in our example) is always greater than the equivalent (0.95% in our case) reflecting the true monthly rate equal to the rate proposed by the bank.

Returning to our example, it suffices to replace in the formula Vn values: t = 0.95%, n = 60 and V n = 50 000 to find the amount has it takes place monthly for 5 years.

So if I put a monthly amount of 622.12 euro at the rate of 12% would have after the fifth year due to 50 000 Euro 37 Euro 327.2 (= 622.12 x 60) repayment installments and the rest placed 12 672.8 Euro as interest on investments.

More practical cases for calculating loans further.

Response to Comments:

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To answer your question, we apply the formula of earned value cited below as shown on the image below:
This formula gives us what I would have at the end of the Xth year of an investment of 1 € monthly at annual T%.

If I place 1 € every 3 months, I would replace T% / 12% by T / 4 and 12.X by 4.X.