 # Simple Interest vs. Compound Interest

If you have applied for a loan or a sure financial product that you already know about simple interest vs. compound interest, here we will define these concepts, the differences between them, the characteristics and some examples of simple interest and compound interest, so that you do not have no doubt. How does simple interest and compound interest work? What is interest? We use interest to measure the profitability of savings and investments. Also to measure the cost of a bank loan. This cost is represented as a percentage referred to the total of the investment or credit. Knowing the difference between simple interest and compound interest is necessary to understand the economic movements that we are going to make or plan to make.

Simple interest It is the interest or benefit that a company obtains from an investment that it has made or sold and that can be financial or capital when the interest produced during each period that the investments last is due only to the initial capital since the benefits are withdrawn after the expiration of each period. This means that the interest is only calculated on the capital or initial amount, not on the productive capital or profits. The concept of interest is related to the price of money.

If a loan is requested, a certain interest must be paid for that money. If you deposit money in a bank, the bank must pay some interest for that money. The simple interest is calculated and paid on the initial capital that will remain unchanged. Several parties intervene in this business:

Capital: It is not more than the amount of initial money, the one that we lend, invest or deposit.

Rate: It is the amount of money that is paid for each 100% of the capital.

Time: It is the time during which the money will generate interest.

Interest: This is the amount of money that will be charged or paid for the use of the capital during the time.

The simple interest is always calculated on our initial capital. Therefore, the interest we are obtaining is not reinvested in the next period. Therefore, the interest obtained in each period is the same.

Simple Interest Formula

Next we will see the simple interest formula and its components: VF = VA (1 + n * i)

•VF = Future Value

•VA = Current Value

•i = Interest rate

•n = Period of time

We can obtain the interest produced by a capital with the following formula: I = C * i * n For example if we want to calculate the simple interest produced by a capital of 30,000 pesos invested during 5 years at a rate of 8% per year. The simple interest will be calculated in the following way: I = 30,000 * 0.08 * 5 = 12,000 If we want to calculate the same interest during a period of less than one year (60 days) , it will be calculated as follows: Period: 60 days = 60/360 = 0.16 I = 30,000 * 0.08 * 60/360 = 384.

Compound interest represents the accumulation of interest that has been generated in a given period of time by an initial capital at an interest rate during certain periods of taxation. In this way, the interest obtained at the end of each investment period is not withdrawn but is reinvested or added to the initial capital, that is, capitalized. It is the interest rate that is charged for a credit and that when liquidated is accumulated to the capital, so in the next settlement the previous interest will be part of the capital and will be a basis for calculating the new interest.

In the compound interest , the interests that we obtain in each period are added to the initial capital, with which they generate new interests. Here unlike simple interest, interest is not paid at maturity, because it evades cumulative capital. Therefore, capital grows at the end of each of the periods and the interest calculated on a larger capital also grows. Next we will see the compound interest formula and its components: VA = VF (1 + i) ^ n

•VF = Future Value

•VA = Current Value

•i = Interest rate

•n = Period of time

Simple and Compound Interest Rates: Characteristics

The characteristics of the simple interest rate are:

•The initial capital is the same during every operation.

•It is the same interest for each of the periods of the operation.

•We apply the interest rate on the invested capital or initial capital.

The characteristics of the compound interest rate are:

•The initial capital increases in each period because the interests add up.

•We apply the interest rate on a capital that varies

•Each time the interests are greater

Differences between simple interest and compound interest The main differences between simple interest and compound interest are:

•In the simple interest the initial capital is the same throughout the operation, while in compound interest this capital varies in each period.

•In the simple interest the interest is the same, while in the compound interest the interest varies in each period. In short, the main difference is whether or not the interests caused are reinvested periodically. With the compound interest the interests are reinvested and therefore, every time we are getting greater benefits. While with simple interest, interest is not reinvested and we always get the same amount.

•The simple interest is the profit that is calculated based on a percentage on an initial capital. The profit that it generates is withdrawn, that is, it is not reinvested in the initial capital.

•Compound interest represents the cost of money and the profit or utility of an initial capital at an interest rate during a period during which the interest obtained at the end of each period is reinvested and added to the initial capital producing a final capital.

What is simple capitalization?

“Simple capitalization” is based on the future determination of a capital using a non-cumulative formula . That is, the initial capital generates some interests, but these are not added to that amount to calculate their future returns. In other words: returns are always generated based on the original capital. The process is fairly simple. It can be used in investments or when a loan is in the deficiency phase , that is, when only interest is paid. The formula is applied mainly in investments with a duration equal to or less than one year (in the short term). However, the period can be extended for a longer time.

To determine the interest obtained (I) 3 fundamental factors are used: initial capital (C0), interest rate (Ti) and investment time (t): I = C0 x Ti xt For example, if we have an initial capital of \$1,000 with an interest rate of 7% for one year, we would perform this operation : “1,000 x 0,07 x 1”, which would tell us that at the end of the year we would have created \$70 of interests. Now, if we add this amount to the initial capital, we obtain the final capital: 1,000 + 70 = 1,070 dollars. With this we would have completed the complete formula: Final capital = C0 + (Co x Ti xt) For the calculation to be correct, we must apply the interest rate and the time of the investment in the same temporary unit (in this case, years). If we had wanted to calculate in months we would have to divide the annual percentage by 12, with what the formula would have been like this: 1,000 x 0.005983 x 12 = 70. With this formula we can also perform the inverse calculation to determine what was the interest according to the final and initial capitals.

What is compound capitalization?

Unlike what happens with the calculation of simple capitalization, “compound capitalization” includes productive interests . That is to say, that the initial capital generates interest that is added to this amount to generate new returns. For the calculation, the same variables are taken into account as with the formula previously described. Let’s imagine that, again, we have an initial capital of \$1,000 with an interest rate of 7% a year; but this time under the compound capitalization law. Will we get the same performance? Logic tells us not, but in periods of one year the interest generated is the same in both formulas . We start with the calculation, which now has this form: It can be applied to various financial products and investments , especially to investment funds, deferred capital insurance products and pension plans ; it is not usually applied in the calculation of mortgage loans. To better understand this term let’s see it with an example. Final capital = C0 x ((1 + Ti) ^ t) ^ t = high for the period of time. In this way, we have 0.07 + 1 = 1.07 that we raise for the time (1 year) and multiply it by the \$1,000 of the initial capital. This gives us the same result as with simple capitalization. That is, \$70 of interest that when adding to the initial capital gives us 1,070 final capital.

The differences will be noticed in different periods of the year. In the case of periods lower than this, the simple capitalization will give us interests higher than the formula of compound capitalization; the opposite will happen in higher periods . For this reason, the most logical thing is that in the case of investments with periods of up to one year, simple capitalization is applied and, from that point, composite capitalization calculations are used.

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