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Simple and Compound Interest including Annuity-Applications

Simple Interest

Objective After going through this lesson, you shall be able to understand the following concepts. Why Interest Is Paid Definition of Interest and Related Terms Simple Interest and Its Formula Introduction Mohan is a shopkeeper. He owns a stationary shop. Once, he borrowed Rs 10,000 from a money lender for three months to buy stationary items. After three months, he returned the borrowed money to the moneylender. Did he pay only the borrowed money to the moneylender?  The answer is 'No'. He paid Rs 2,000 more to the moneylender along with Rs 10,000 after three months. The extra money paid to the moneylender is called the interest. In this lesson, we will learn the concepts of interest. Why Interest Is Paid Now, if Mohan borrowed Rs 10,000 from a moneylender for three months, then why does he need to pay Rs 2,000 more to the moneylender. What is the need to pay the extra sum of money? There are many reasons to it. Let us discuss the following reasons in detail: Time value of money: Nowadays, the cost of almost all items is increasing with time. So, in order to purchase the same item in future, we need to pay more money for it. In other words, we can say that the value of money is decreasing with time. For this reason, we have to pay extra money on the borrowed sum of money. Opportunity Cost: A person may have many options to invest his money. He may earn profit by investing his money in some business or earn money by depositing the money in the bank. But, by lending his money, he loses on the profit or the extra money which he gets from the bank. So, to incur his loss, the lender would charge extra money. Risk factor: There is always a risk that the borrower may run away or he may become bankrupt. Therefore, interest is taken to cover the risk. Definition of Interest and Related Terms Interest: Interest is the extra money paid by the borrower to the lender for using his money for a specified period of time. Mohan borrowed Rs 10,000 from a moneylender for three months. He paid Rs 2,000 more to the money lender along with Rs 10,000 after three months. This extra Rs 2,000 paid to the money lender is the interest. Principal: Principal is the original sum of money borrowed or lent. It is generally denoted by P.  The amount of Rs 10,000 borrowed by Mohan from the moneylender is the principal. Time: Time is the duration for which the money is borrowed or lent. Generally, the time is expressed in years and is denoted by T. This may be expressed in months and days also. Mohan borrowed Rs 10,000 from a money lender for three months. Here, three months is the time. Rate of interest: The rate at which the interest is calculated for a defined period of time on the principal is known as the rate of interest. It is generally denoted by R. The rate of interest is usually expressed as percentage. The rate of interest paid on the borrowed or lent sum of money is agreed upon by the borrower and the lender. Amount: Amount is the sum of Principal and Interest. It is generally denoted by A. Mohan borrowed Rs 10,000 from a moneylender for three months. He paid Rs 2,000 more to the money lender along with Rs 10,000 after three months. Total money received by the money lender = Rs 10,000 + Rs 2,000 = Rs 12,000 Here, Rs 12,000 is the amount. Simple Interest and Its Formula When the interest is calculated every year on the original amount of money, that is, the principal, such interest is called simple interest. Even though, the interest may get accumulated year after year, but this accumulated interest is not considered for calculating the interest for later years. No interest is paid on the interest earned during the term for which the money is borrowed or lent. Simple interest can be calculated by using the following formula: Simple interest = Principal × Rate × Time 100 = PRT100 Amount = Principal + Simple interest = P+PRT100 = P1+RT100 Let us solve some examples to understand the concepts.

Example 1: An amount of Rs 25,200 was deposited in a bank. If the bank paid interest at the rate of 8% per annum, then what is the interest received at the end of 3 years? ​Solution Principal, P = Rs 25,200 Rate of interest, R = 8% per annum Time, T = 3 years

Thus, the interest received at the end of 3 years is Rs 6,048.

Example 2: Riya borrowed some money from her friend at the rate of 6.5% p.a in simple interest. She paid Rs 1,066 as a simple interest for 2 years. What is the sum of money that Riya had borrowed from her friend?

Solution Given: Simple interest = Rs 1,066 Rate = 6.5% p.a. Time = 2 years

Thus, the sum of money that Riya had borrowed from her friend is Rs 8,200.

Example 3: Suresh borrows a sum of Rs 31,250 from a bank. He repays the amount together with the interest of Rs 6,875 at the end of 4 years. Find the rate of interest. ​Solution Here, Principal, P = Rs 31,250 Time, T = 4 years Simple interest = Rs 6,875 We have to find the rate of interest (R). We know S.I. = Thus, the required rate of interest is 5.5% per year.

Example 4: A sum of Rs 18,450, when deposited in a bank, amounts to Rs 22,140. If the bank provides interest at the rate of 4% per annum, then what is the time period for which the sum is deposited in the bank? ​Solution Given: Principal, P = Rs 18,450 Amount, A = Rs 22,140 A = S.I. + P ⇒ S.I. = Rs 22,140 − Rs 18,450 = Rs 3,690 Let T be the number of years. Thus, the required time period is 5 years.

Example 5: A certain sum of money becomes five times at the end of n years when the interest is provided at the rate of 10% per annum. What is the value of n? Solution​ Let P be the principal. Given: Amount, A = 5P ∴ S.I. = A − P = 5P − P = 4P We know S.I. Rate of interest, R = 10% per annum Time, T = n years ∴ 4P Thus, the value of n is 40.

Objective After going through this lesson, you shall be able to understand the following concepts. Why Interest Is Paid Definition of Interest and Related Terms Simple Interest and Its Formula Introduction Mohan is a shopkeeper. He owns a stationary shop. Once, he borrowed Rs 10,000 from a money lender for three months to buy stationary items. After three months, he returned the borrowed money to the moneylender. Did he pay only the borrowed money to the moneylender?  The answer is 'No'. He paid Rs 2,000 more to the moneylender along with Rs 10,000 after three months. The extra money paid to the moneylender is called the interest. In this lesson, we will learn the concepts of interest. Why Interest Is Paid Now, if Mohan borrowed Rs 10,000 from a moneylender for three months, then why does he need to pay Rs 2,000 more to the moneylender. What is the need to pay the extra sum of money? There are many reasons to it. L

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