Simple and Compound Interest - Essay Example

Simple and Compound Interest Introduction Interest is an amount paid for utilization of borrowed money. A borrower pays interest to the lender for credit or any other comparable liability. In other words, interest happens to be charge for a privilege of borrowing cash. Borrowing is important in everyday life since it is a source of funding that facilitates undertaking of projects. Important examples of interest in real life include interest pain on bank loans, bond yields, as well as return on savings. The difference between interest and profit is that profit is yield as a result of investment (to an owner) while interest is paid to a lender. This paper looks at the differences between the two basic interest types: Simple Interest and Compound Interest. Whether one is paying interest or being paid interest, a matter of significance is to know how interest is computed. There are two key types of interest: simple interest & compound interest. The manner in which each of the two interests is calculated affects the entire amount paid out. Understanding both forms of interest is important since they impact interest payments a person receives or makes. Each of them is calculated differently hence amount paid in the long run is different. Simple interest Simple interest is interest expressed as a percentage of principal or the original amount borrowed or lent, for the entire period of borrowing. The interest will be the income received with regard to the lending or the price paid for the utilization of borrowed amount. Simple interest happens to be the fastest as well as easiest approach of computing the interest on amount borrowed or lend. A car loan is a very popular example of simple interest, with which interest is charged only on the principal or original amount borrowed or lent. Below is the formula utilized in calculating interest owed in simple interest: Simple interest = P*r*n In the above formula, P = Principal amount or the initial amount deposited or borrowed = rate of interest, and n = number of years Example If a person borrows $1,000 from friend, @ 10% per annum for three years, then the computation for simple interest will as follows: Simple interest – P*r*n I = 1,000 * 0.1 * 3 I = 300 The borrower will pay $1,300 to the lender at the end of year 3. This will be $1,000 the principal amount borrowed and $300 the interest charged for keeping the amount. $1,300 is known as the Amount. It is important to understand that keeping the amount for periods means higher interest. For instance, in the above example, if the borrower was to keep the money for five years, the interest would be: I = 1,000 * 0.1 * 5 Interest = 500. The Interest would be $500 making the Amount to be $1,500. Compound interest Compound interest is interest expressed as a percentage of the revised principle. In other words, compound interest may be referred to as interest added to the principal amount of a loan or deposit in order for the interest added to also earn interest onwards. In this approach, interest earned within the prior periods is added to the initial amount/principal: this increases the amount, on which the next period’s interest will be charged. The summing up of the principal amount and the interest is referred to as compounding. In this case, interest has to be paid on principal amount as well as interest accumulated during the deposit or loan term. Conversion period Conversion period is the time interval between 2 interest payment periods. The table below shows how interested is compounded at the end of conversion periods: Conversion Period Compounded One Day Daily One Week Weekly One Month Monthly Three Months Quarterly Six Months Semi-Annually Twelve Months Annually It happens to be normal for banks to pay interest on semi -annually basis. Financial institutions, on the other hand, have a guiding principle of paying interest on quarterly basis. It is important to understand to how to calculate compound interest. The formula for computing compound interest Compound interest formula is A = P (1 + r/n) ^ nt In the above formula; P – Principal amount or the initial amount deposited or borrowed r = rate of interest per annum (as a decimal) t = the number of periods or years the amount is borrowed for or deposited n = the number of times that interest is compounded per year A = amount of money that has accumulated after n years with interest included. Example A loan of $10,000 is charged at 5% interest for 3 years compounded annually, then compound interest is calculated as follows: P = 10,000 R = 5% n = 1 T = 3 Simple interest = [P (1 + I) n] – P = P [1 + I) n-1] $10,000[(1 + 0.05)3]-1 = $10,000[1.157625 – 1] =$ 1,576.25 Year Opening balance Interest@ 5% Closing Balance 1 10,000 500 10,500 2 10,500 525 11,025 3 11,025 551.25 11,576.25 Total Interest 1,576.25 Below is Table of Comparison (simple interest against compound interest) Basis of comparison Compound Interest Simple Interest Meaning Compound interest is interest that is computed as a percentage of both principal and accumulated interest. Simple interest is interest hat is computed as a percentage of principal amount only Formula Compound Interest= P*(1+r)^nk Simple Interest=P*r*n Principle Keeps on changing throughout the whole borrowing period Constant throughout the period Return Comparatively high less Growth Increases quickly Remains uniform Interest Charged on Principal + accrued interest principal Main Differences between Compound Interest and Simple Interest The following are the key differences between the two forms of interest: 1. Interest charged on principal amount for the whole loan term is referred to as Simple Interest. On the other hand, interest calculated based on both the principal amount plus interest earned previously is referred to as Compound Interest. 2. Simple interest gives low return as compared to compound interest 3. Simple interest growth rate happens to be lower in comparison to compound interest 4. The principal keeps on changing from period to the other in compound interest due to the compounding effect, while principal remains constant within simple interest 5. The calculation of compound interest is quite complex while that one for simple interest is easy Conclusion Interest is the fee charge on utilizing another individual’s money. Various reasons exists as to why interest has to be paid, for instance, opportunity cost as well as risk factor, inflation, and the time value for money. Compound interest happens to be practically challenging to compute while simple interest is easy and quick to compute. On calculating both compound interest and simple interest on a specified Principal, Rate, as well as Time, compound interest will at all times emerge to be higher compared to simple interest mainly due the effect of compounding. Reference Gosling, J. (1995). Maths for Business and Finance. Pascal Press. Read More