# Difference between simple interest and compound interest pdf

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- Simple Interest vs Compound Interest
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- Difference Between Simple Interest and Compound Interest

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There are two different ways of calculating interest -- simple and compound. Here's how to calculate each, as well as the key differences and similarities between the two. Simple interest Simple interest is well, simple. Each year, the interest is calculated as a percentage of the principal, as follows:.

## Simple Interest vs Compound Interest

Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest. It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal sum plus previously accumulated interest. Compound interest is standard in finance and economics.

Compound interest is contrasted with simple interest , where previously accumulated interest is not added to the principal amount of the current period, so there is no compounding. The simple annual interest rate is the interest amount per period, multiplied by the number of periods per year. The simple annual interest rate is also known as the nominal interest rate not to be confused with the interest rate not adjusted for inflation , which goes by the same name.

The compounding frequency is the number of times per year or rarely, another unit of time the accumulated interest is paid out, or capitalized credited to the account , on a regular basis.

The frequency could be yearly, half-yearly, quarterly, monthly, weekly, daily, or continuously or not at all, until maturity. For example, monthly capitalization with interest expressed as an annual rate means that the compounding frequency is 12, with time periods measured in months. The nominal rate cannot be directly compared between loans with different compounding frequencies.

Both the nominal interest rate and the compounding frequency are required in order to compare interest-bearing financial instruments. To help consumers compare retail financial products more fairly and easily, many countries require financial institutions to disclose the annual compound interest rate on deposits or advances on a comparable basis.

The interest rate on an annual equivalent basis may be referred to variously in different markets as effective annual percentage rate EAPR , annual equivalent rate AER , effective interest rate , effective annual rate , annual percentage yield and other terms. The effective annual rate is the total accumulated interest that would be payable up to the end of one year, divided by the principal sum. The total compound interest generated is the final value minus the initial principal: [4].

This is very unusual in practice. The interest is less compared with the previous case, as a result of the lower compounding frequency. Since the principal P is simply a coefficient, it is often dropped for simplicity, and the resulting accumulation function is used instead. Continuous compounding can be thought of as making the compounding period infinitesimally small, achieved by taking the limit as n goes to infinity. See definitions of the exponential function for the mathematical proof of this limit.

The amount after t periods of continuous compounding can be expressed in terms of the initial amount P 0 as. In mathematics, the accumulation functions are often expressed in terms of e , the base of the natural logarithm.

This facilitates the use of calculus to manipulate interest formulae. For any continuously differentiable accumulation function a t , the force of interest, or more generally the logarithmic or continuously compounded return is a function of time defined as follows:. This is the logarithmic derivative of the accumulation function.

When the above formula is written in differential equation format, then the force of interest is simply the coefficient of amount of change:. For compound interest with a constant annual interest rate r , the force of interest is a constant, and the accumulation function of compounding interest in terms of force of interest is a simple power of e :. The force of interest is less than the annual effective interest rate, but more than the annual effective discount rate.

It is the reciprocal of the e -folding time. See also notation of interest rates. The interest on loans and mortgages that are amortized—that is, have a smooth monthly payment until the loan has been paid off—is often compounded monthly.

The formula for payments is found from the following argument. This can be derived by considering how much is left to be repaid after each month. The Principal remaining after the first month is. If the whole loan is repaid after one month then. This is a geometric series which has the sum. A formula that is accurate to within a few percent can be found by noting that for typical U. In terms of these variables the approximation can be written.

The expansion. Given an principal initial deposit and a recurring deposit, the total return of an investment can be calculated via the compound interest gained per unit of time.

If required, the interest on additional non-recurring and recurring deposits can also be defined within the same formula see below. If two or more types of deposits occur either recurring or non-recurring , the compound interest earned can be represented as. Compound interest was once regarded as the worst kind of usury and was severely condemned by Roman law and the common laws of many other countries.

The Florentine merchant Francesco Balducci Pegolotti provided a table of compound interest in his book Pratica della mercatura of about Richard Witt 's book Arithmeticall Questions , published in , was a landmark in the history of compound interest. It was wholly devoted to the subject previously called anatocism , whereas previous writers had usually treated compound interest briefly in just one chapter in a mathematical textbook. Witt was a London mathematical practitioner and his book is notable for its clarity of expression, depth of insight and accuracy of calculation, with worked examples.

In the 19th century, and possibly earlier, Persian merchants used a slightly modified linear Taylor approximation to the monthly payment formula that could be computed easily in their heads. From Wikipedia, the free encyclopedia. A compounding sum paid for the use of money.

See also: Logarithmic return. See also: Day count convention. This section needs additional citations for verification. Please help improve this article by adding citations to reliable sources.

Unsourced material may be challenged and removed. The Interest Act specifies that interest is not recoverable unless the mortgage loan contains a statement showing the rate of interest chargeable, "calculated yearly or half-yearly, not in advance. Retrieved James and John Knapton, et al. Cambridge, Massachusetts. Journal of the Institute of Actuaries. Mathematics Magazine.

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Natural logarithm Exponential function. John Napier Leonhard Euler. Schanuel's conjecture. Wikiquote has quotations related to: Compound interest. Look up interest in Wiktionary, the free dictionary.

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Interest is the fees paid by the borrower to the lender for borrowing money. For example, banks charge interest on the loans taken by the customers. People deposit money in the banks to earn interest on the amount deposited. Higher interest rates higher is the opportunity for investors to earn higher rates of return. There are two ways to calculate the interest on the principle: Compound and the Simple interest.

Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest. It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal sum plus previously accumulated interest. Compound interest is standard in finance and economics. Compound interest is contrasted with simple interest , where previously accumulated interest is not added to the principal amount of the current period, so there is no compounding. The simple annual interest rate is the interest amount per period, multiplied by the number of periods per year.

The interest rate is mutually decided by both the parties. Interest can be charged in two ways, i. The former is the type of interest where the interest is charged only on loaned amount but in the case of the latter interest is calculated on the amount lent plus accumulated interest. So, simple interest is the sum paid for using the borowed money, for a fixed period. On the other hand, whenever the interest becomes due for payment, it is added to the principal, on which interest for the succeeding period is reckoned, this is known as compound interest.

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There are two ways for a lender to charge interest on a loan , which are the simple interest and compound interest methods. Simple interest is calculated based solely on a percentage of the loaned amount, while compound interest is calculated based on a percentage of the loaned amount and interest. The higher the frequency of compounding, the higher the return will be for the lender. These variations in how the calculation is derived result in the following differences:. Amount charged.

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### Difference Between Simple Interest and Compound Interest

Anyone who takes out a loan has to think about the cost of doing so. Interest can be simple or it can compound over time. Check out our investment calculator. The term interest indicates how much you can earn from the money you originally invest. As your investment sits in an account over time, interest accumulates and you can watch your funds grow. To calculate the amount of simple interest you stand to earn as an investor, you can use the following formula: Principal Balance x Interest Rate. A is the amount you have after compounding.

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