All organizations, companies, groups or individuals need at some point to obtain funds to finance themselves, these funds are usually very difficult to obtain and when they are reached, the entities or persons who make these loans receive a fee for the time that the money is in the hands of its debtors.
The issue of interest charged by lending agents to companies is very important today, since these are the main source of obtaining resources in the short term, so it is necessary to do a little analysis of the amounts that are returned to the lenders and the way of calculating them, since the interest that is charged for one or another loan can vary its amount according to factors that will be subsequently expressed.
Interest to be defined
Interest is all that benefit, gain, rent, utility or profit that is paid to use money provided by third parties, it is the remuneration for a service provided, in almost all financial activities carried out between two natural or legal persons it is considered as a canon of behavior charging interest when borrowing cash.
What is interest?
Interest is all that profit, utility or profit produced by capital.
Interest can depend on three fundamental factors: Capital, Interest Rate and time.
- Capital (p): It is the amount of money that is initially loaned. Interest rate (i): It is the amount of money that is paid for the loan of the capital, almost always it is expressed as a percentage. Time (t): It is the duration of the loan.
Simple interest
Simple interest is a direct function between time, the interest rate and the initial capital, this is represented by the formula:
I = pit
Example 1. Calculate the simple interest charged on a $ 100 loan at a rate of 6% per year.
RTA /
I = pit
I = 100 * 6% * 1
I = 6
This means that at the end of the year you must pay an interest of $ 6
Simple interest classes:
- Ordinary: It is one that is calculated over 360 days per year. Exact: It is one that is calculated with 365 or 366 days depending on the case.
Example 2. Calculate the ordinary simple and exact interest of a loan made by an entity for the sum of $ 400 with an interest of 20% during one year.
RTA /
Ordinary I = 400 * 20% * 30/360
Ordinary I = 6.66
I Exact = 400 * 20% * 30/365
I Exact = 6.57
It can be seen that with ordinary simple interest a greater amount of money is paid than in the exact one, in cases like the previous one where the sums are small, the difference is laughable, but in larger amounts this can become a source of more payments. high.
The fundamental difference between simple interest and compound interest is that in the former the capital remains constant, and in the latter the capital changes at the end of each time period.
Compound interest
Compound interest is that amount obtained by the loan, when the money received from the initial capital becomes part of that same capital at the end of the first period of time, this is done to form a new capital and on this will cause the new interests. Compound interest can be expressed:
S = p (1 + i) n
Where:
S = Final capital
p = Initial capital
i = interest rate
n = Number of periods
Example 3. Calculate the final value of a principal of $ 700 at a rate of 25% for 5 years.
RTA /
S = p (1 + i) n
S = 700 (1 + 0.25) 5
S = 2136.23
This would be the amount obtained at the end of the fifth year.
Example 4. Find the accumulated values of the previous year at the end of each year.
|
Period |
Initial capital |
Interest |
Final capital |
|
one |
700 |
175 |
875 |
|
two |
875 |
218.75 |
1,093.75 |
|
3 |
1,093.75 |
273.4375 |
1,367.1875 |
|
4 |
1,367.1875 |
341.796875 |
1708,98438 |
|
5 |
1708,98438 |
427,246094 |
2,136,23047 |
Having already the bases and the general theory of simple interest and compound interest, we must now see how each one is paid, this is reflected in the type of interest rate that is paid in each period of time.
Effective Rate:
The effective rate is that rate that is calculated for a given period and that can cover intermediate periods, is represented by (i).
Nominal Rate:
The nominal rate is that which is given for one year, it is represented by (j). This must be converted into effective, so that it can be applied in the interest formula.
Period:
The time that elapses between the payment of interest. The total of periods is represented by the letter (n), and the periods that are presented within that total are represented by the letter (m), from this we must divide the total by the number to find the rate of the period of periods like this:
i = j / m
Example 5. Find the final principal of a sum of $ 35,000 with an interest of 20% convertible quarterly for 2 years.
RTA / First we find the effective rate.
i = j / m
i = 20% / 4
i = 5% quarterly cash
Now the final capital will be found with the formula proposed for compound interest, bearing in mind that in two years there are 8 quarters.
S = p (1 + i) n
S = 35000 (1 + 0.05) 8
S = 51710.94
Example 6. Calculate the 10-year principal of $ 120,000 with interest of 24% convertible semi-annually.
RTA /
i = j / m
i = 24% / 2
i = 12% cash semiannual
S = p (1 + i) n
S = 120000 (1 + 0.12) 20
S = 1157555.17
The study of interest as seen above is of vital importance to calculate well the obligations that we can acquire, since we can anticipate the future, and analyze if the loans that third parties make us are feasible to pay, this is a basic approach to the study of financial mathematics, next articles will deal with topics related to the previous one.
