Lesson Basics of Interest Rates and its uses

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This Lesson (Basics of Interest Rates and its uses) was created by by Shruti_Mishra(0)

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About Shruti_Mishra: I am a maths graduate from India and am currently persuing masters in Operations Research.

What is <A href="interest.wikipedia">interest</A>?

<A href="interest.wikipedia">Interest</A> is basically the fee which is paid by the borrower for borrowing the money from the lender. Borrower is the person who takes some money for his use and pays fee for keeping the money to him. Lender is the one who lends the money to the other person and charges for lending his money.

At one point of time a person can be both the lender and the borrower. Let�s make the picture clearer by considering an example. Suppose �A� lends the money to �B� who in turn lends the money to� C�.  So at one point of time �B� is both the lender and the borrower. For �A� he is the borrower and for �C� he is the lender.

Types of <A href="interest.wikipedia">interest</A>

The basic figure (principal) on which we charge the interest every year depends on the agreement on which we are lending the money.

�Let�s analyze what happens when sum of 100 has been lend for a period of three years at the rate of 10%�

In this case there can be two kind of agreement in which a person can enter.
1: If the person agrees to charge interest on the fixed amount of money every year, it is the case of <A href="simple_interest2.lesson">Simple Interest</A> i.e. 10% rate of interest will be charged for the next three year on Rs 100 (0.10 * 100 = 10)
The total interest earned during the three years is 10 + 10 + 10 = 30
2: If the person earns interest on the interest which he earns every year then it is the case of <A href="compound_interest2.lesson">Compound Interest</A>.

Example: A lends Rs 100 to B and charges <A href="compound_interest2.lesson">compound interest</A> at the rate of 10%. In the first year A earns an <A href="interest.wikipedia">interest</A> of Rs 10. Next year B will give A the fixed <A href="interest.wikipedia">interest</A> of RS 10 and an additional sum of Rs 1 which will be the interest on interest earned by him in the first year (10 % of 10 = 1). So the total interest which A will earn in second year is (10 + 1 = 11). It can also be understood in a second way where we add the interest to the principal after the first year. So the principal is now 100 + 10 = 110. The interest calculations for next year will be based on this figure. Hence interest in second year would be 10% of 110 = 11, the same answer as earlier. In the same way, interest in third year will be on principal of 100+10+11 = 121. Thus the total interest after 3 years would be 10 + 11 + 0.1*121 = $33.1

In layman term, in case of simple interest the borrower return backs the interest to the lender every year (or keeps it in a non interest paying account); he is not bound to pay any <A href="interest.wikipedia">interest</A> on it. The <A href="interest.wikipedia">interest</A> is calculated only on the principal. On the other hand, in case of <A href="compound_interest2.lesson">Compound Interest</A>, the Borrower pays the charge for keeping the interest with him i.e. interest on interest, and hence the interest calculation is on the amount outstanding. Compound interest is thus always more than simple interest for the same principal, time and interest rate.
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CI (P,R,T) > SI (P,R,T)
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Interest rate is used in innumerable places in our daily lives. Banks use it to calculate the interest payments on deposit and loan accounts. <A href="financial_institutions.wikipedia">Financial institutions</A> use it to value other opportunities in terms of <A href="NPV.lesson">NPV</A>. Companies use it to calculate the cost of borrowing money required for their operations. <A href="interest_rate.wikipedia">Interest rates</A> prevailing in a country also tell a lot about the economic and financial health of the country.

The following solvers can be helpful for calculations and further understanding:
<A href="simple_interest.solver">
Calculate Simple Interest, given Principal, Time and Interest Rate </A>
<A href="compound_interest_calculation.solver">
Calculate Compound Interest, given Principal, Time and Interest Rate</A>
<A href="calc_SimpleInterestRate.solver">
Calculate Interest Rate, given Principal, Simple Interest and Time</A>
<A href="calc_P_CI.solver">
Calculate Principal if Time, Interest Rate and Compound Interest are given</A>