Financial mathematics

30 December 2008 - 14:12

The financial mathematics allow us to solve problems based on operations of investment (for example, to know the yield a business project) and of financing (for example, to know which is the interest that we must pay by the acquisition of a loan).

Two operations that seems opposite, but that they are the same if they are seen from two different points of view, for example, if we asked for a loan in the bank, we will be conducting an operation of financing, whereas the bank, at the same time, would be conducting an operation of investment.

This article we will not enter depth in the study of the financial mathematics, we will only see the definition of its main elements, so that it as guide serves or reference to us for a later study.

Initial amount

It is the initial amount of the money before being turned to a final amount through a rate of variation, in some cases also is denominated:

• Present value (V.A)
• Capital (c): term used mainly in investments.
• Main (p): term used mainly in banking operations.

Final amount

It is the final amount of the resulting money of to have applied a rate of variation to an initial amount, in some cases also is denominated:

• Future value (V.F)
• Stock (s)
• Amount (m): term used mainly in banking operations and investments.

Rate of variation

Percentage in which it varies an amount (GOES or VF) to the being turned into another one (VF or GOES) in a period of certain time; they are rates of variation:

• Interest rate (i): it is used in the loans, when there is to pay interests by him.
  * (i) is the abbreviation of interest rate and (i%) it is the interest rate in percentage, for example, if “i” = 0,2, then “i%” = 20% (0,2 x 100).
• Rate of yield or yield: it is used in the investments.
• Rate of discount (TD): it is used when it is wanted to update a VF to GOES.

Number of periods or terms (n)

Number of periods in which the financial operation is realized, can be represented in years, months, days, trimesters, etc.

Capitalization

One occurs when the application becomes effective of a rate of variation to GOES, for example, if to 100 a rate of 10% is applied to him, the 110 would be the capitalized value.

Update

One occurs when the application becomes effective of a rate of variation to a VF, for example, if to 110 a rate of 10% discounts to him, the 100 would be the updated value.

Interest (i)

Gain or loss that is obtained when turning GOES to a VF by means of an interest rate; the term interest also is used like synonymous of interest rate.

Yield

It is the gain (interest) that is obtained when turning GOES to a VF through a rate of variation; it can be:

• Fixed yield: obtained yield, for example, when investing our money depositing it in an account of savings, in a bank that pays a TEA.
• Variable yield: obtained yield, for example, investing to our money buying action.

Yield

It makes reference to the rate of variation that is applied to him to GOES, for example, if 100 grow in 110, then we can say that it had a yield of 10%.

Cost of the money

It makes reference to the rate of variation that is applied to him to GOES, for example, if 100 grow in a 10%, is possible to be said that the 100 have a 10% cost; they are money costs:

• interest rate.
• capital cost.

Nominal interest rates (TN)

It is the rate where the period of capitalization is not indicated, when using it, do not capitalize the interests, reason why is used when finding the simple interest.

Effective interest rate (YOU)

It is the rate where yes the period of capitalization is indicated, when using it, yes capitalize (cash become) the interests, reason why is used when finding the composed interest, for example, if it is a TEM, the capitalization is monthly.

Simple interest

In the simple interest, the interest (interest rate) is applied on the capital in all the periods.

For example, if a loan of 1000 to one METRIC TON of 2% by a time of 3 months is realized:

n	Capital	Interest
1	1000	20
2	1000	20
3	1000	20
Total		60

To first, secondly and third month, is pleased (or it receives) by interests, 2% of 1000; to the third month, 1000 (IT GOES) + 60 are pleased (or it receives) (i) = 1060 (VF).

Compound interest

In the compound interest, the interest (interest rate) is applied first on the capital (or loan), and soon on the capitalized amount (capital + interest).

For example, if a loan of 1000 to a TEM of 2% by a time of 3 months is realized:

n	Capital	Interest
1	1000	20
2	1020	20.4
3	1040	20.81
Total		61.21

To the first month 2% of 1000 are pleased (or it receives), to the second month, 2% of 1020 (capitalized amount), to the third month 2% of 1040; to the third month 1000 (IT GOES) + 61,21 would be pleased (i) = 1061,21 (VF).

The VF as a result of applying the compound interest, always will be major that when applying the simple interest.

Interest to refute with decreasing quotas

It is a type of compound interest, where the capitalized amount is not capital + the interest, but the balance that is to deduce to the capital a certain amortization as a result of the payment of a quota (or net flow).

For example, if a loan of 1000 to a TEM of 2% by a time of 3 months is realized:

n	Balance	Amortization	Interest	Quota
1	1000	333.33	20	353.33
2	666.67	333.33	13.33	346.67
3	333.33	333.33	6.67	340
Total	0	1000	40	1040

Interest to refute with fixed quota

He is similar to the previous one, with the difference that first determine a quota, or net, constant flow or fixed, unlike the previous one where first the amortization is determined.

For example, if a loan of 1000 to a TEM of 2% by a time of 3 months is realized, where a monthly payment of 346.75 is due to pay:

n	Quota	Interest	Amortization	Balance
0				1000
1	346.75	20	326.75	673.25
2	346.75	13.46	333.29	339.96
3	346.75	6.80	339.96	0
Total	1040.26	40.26	1000	0

Labels: Concepts, Finances, Tools of business

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Related contents:

1. The true cost of a credit
2. How to calculate the quota of a loan
3. The TIR GOES and
4. How to know how much it is worth a business
5. Definition of yield