Simple Interest is the rate at which we lend or borrow money. In the following section, we will define the important terms and formulae that will help us solve and understand the questions on the simple interest. We will define the concept of Simple interest and use these formulae and definitions to solve questions that we expect will come from this section. Let us begin with the definitions!

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## Simple Interest

When a person lends money to a borrower, the borrower usually has to pay an extra amount of money to the lender. This extra money is what we call the interest. We can express this interest in terms of the amount that the borrower takes initially. If the interest on a sum borrowed for a certain period is reckoned uniformly, then it is called simple interest or the flat rate. Before starting the formula for the simple interest, let us first state some terms that weÂ will use in the formula.

Principal: The money borrowed or lent out for a certain period is called the principal or the sum.

Interest: Interest is the extra money that the borrower pays for using the lender’s money.

**Browse more Topics under Si And Ci**

- Compound Interest with a Fractional Rate
- Data Sufficiency
- Difference Between Compound Interest and Simple Interest
- SI and CI Practice Questions

*But What is the Difference Between Simple Interest and Compound Interest?*

### Formula For The Simple Interest

Let the principal amount be equal to P. Let the rate at which the interest is levied is equal to R% per annum (per year). let the time for which the amount is lent = T years. Then we can write:

Simple Interest = [{PÃ—RÃ—T}/100]

We can also calculate the Principal amount as P = [{100Ã—(Simple Interest)}/(RÃ—T)].

Similarly, we can write the time T as equal to T = [{100Ã—(Simple Interest)}/PÃ—R].

Now let us solve some examples to get acquainted with these formulae.

Example 1: Find the simple interest on Rs. 68,000 at 16(2/3)% per annum for a period of 9 months?

A) Rs. 8500Â Â Â Â Â Â Â Â Â B) Rs. 3200Â Â Â Â Â Â Â Â Â C) Rs. 2100Â Â Â Â Â Â Â Â Â D) Rs. 4300

Answer: Here, P = Rs. 68000, R = 50/3% per annum and T = 9/12 years = 3/4 years. Note that the time has been converted into years as the rate is per annum. The units of rate R and the time T have to be consistent. Now using the formula for the simple interest, we have:

S.I. =Â [{PÃ—RÃ—T}/100]; therefore we may write: S.I. = Rs. [68000Ã—(50/3)Ã—(3/4)Ã—(1/100)] = Rs. 8500.

In some cases the days of the start and the days when we calculate the interest are present. We don’t count the day on which we deposit the money. However, we do count the day on which we withdraw the money.

*Â Practice Questions for Simple Interest here.*

## Solved Examples For You

Example 3: Khan borrows some money at the rate of 6% p.a. for the first two years. He borrows the money at the rate of 9% p.a. for the next three years, and at the rate of 14% per annum for the period beyond five years. If he pays a total interest of Rs. 11400 at the end of nine years, how much money did he borrow?

A) Rs. 12000Â Â Â Â Â Â Â Â B) Rs. 21000Â Â Â Â Â Â Â Â Â C) Rs. 37000Â Â Â Â Â Â Â Â Â D) Rs. 63000

Answer: Let ‘x’ be the sum that Khan borrows. Then the total simple interest that Khan pays is the sum of the interests. We can write from the formula of the simple interest, [xÃ—6Ã—2]/100 + [xÃ—9Ã—3]/100 + [xÃ—14Ã—4]/100 = Rs. 11400.

Therefore we can write, 95x/100 = 11400 or x = Rs. 12000 and hence the correct option is A) Rs. 12000.

Example 4: The simple interest on a certain sum of money for 2(1/2) years at 12% per annum is Rs. 40 less than the simple interest on the same sum for 3(1/2) years at 10% per annum. Find the sum.

A) Rs. 600Â Â Â Â Â Â Â Â Â Â B) Rs. 666Â Â Â Â Â Â Â Â C) Rs. 780Â Â Â Â Â Â Â Â D) Rs. 800

Answer: Let the sum be Rs. a. Then we can write: [{xÃ—10Ã—7}/{100Ã—2}] – [{xÃ—12Ã—5}/{100Ã—2}] = 40.. This can be written as: 7x/20 – 3x/10 = 4o. Therefore we have x = Rs. 800

Hence the sum is Rs. 800 and the correct option is D) Rs. 800.

Example 5: A man took a loan from a bank at the rate of 12 % p.a. simple interest. After three years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was:

A) Rs. 12000Â Â Â Â Â Â Â Â Â B) Rs. 11000Â Â Â Â Â Â Â Â Â Â C) Rs. 14000Â Â Â Â Â Â Â Â Â Â Â Â Â D) Rs. 15000

Answer: Here we have, the principal = Rs. [{100Ã—5400}/{12Ã—3}] = Rs. 15000. Thus the correct option is D) Rs. 15000.

Example 6: Khan invests a certain amount in three different schemes A, B and C with the rate of interest 10% p.a., 12% p.a. and 15% p.a. respectively. If the total interest that accumulates in one year was Rs. 3200 and the amount he invests in schemeÂ C was 150% of the amount he invests in Scheme A and 240% of the amount he invests in Scheme B, what was the amount he invests in scheme B?

A) Rs. 4000Â Â Â Â Â Â Â Â B) Rs. 5000Â Â Â Â Â Â Â Â C) Rs. 6000Â Â Â Â Â Â Â Â Â Â Â Â D) Rs. 7000

Answer: Let x, y and z be the amounts that Khan invests in schemes A, B and C respectively. Then, we can write using the formula for S.I., : [{xÃ—10Ã—1}/100] + [{yÃ—12Ã—1}/100] + [{zÃ—15Ã—1}/100] = Rs. 3200. Also, we have the conditions that 10x + 12y + 15z = Rs. 320000.

Now, we have z = 240% of y = (12/5)y. And, z = 150% of x = (3/2)x or in other words we can write:

x = (2/3)z = [(2/3)Ã—(12/5)]y = (8/5)y.

Combining the above equations, we have:

16y + 12y + 36y = Rs. 320000 or in other words, we can write 64y = Rs. 320000 and y = Rs. 5000.

Therefore the sum that Khan invests in scheme B = Rs. 5000 and the correct option is B) Rs. 5000.

## Practice Questions

Q 1: Divide Rs. 2379 into 3 parts so that their amounts after 2,3 and 4 years respectively may be equal, the rate of interest is 5% per annum at simple interest. The first part is:

A) Rs. 969Â Â Â Â Â Â Â Â Â B) Rs. 828Â Â Â Â Â Â Â Â Â C) Rs. 890Â Â Â Â Â Â Â Â Â Â Â Â Â Â D) Rs. 234

Answer: B) 828

Q 2: An amount of Rs. 100000 is invested in two types of shares. the first yields an interest of 9% p.a. and the second, 11% p.a. If the total interest at the end of one year is 9(3/4)%, then the amount invested in each share was:

A) Rs. 62500; Rs. 37500Â Â Â Â Â Â Â Â Â Â Â B) Rs. 5733; Rs. 7865Â Â Â Â Â Â Â Â C) Rs. 7297; Rs. 9865Â Â Â Â Â Â Â Â Â D) Rs. 5242; Rs. 8906

Ans: A)Â Rs. 62500; Rs. 37500

. Ajay invested half of his savings in a mutual fund that paid simple interest for 2 years and received Rs. 550 as interest. He invested the remaining in a fund that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest received Rs. 605 as interest. What was the value of his total savings before investing in these two bonds? how to solve this type of problems