### Importance of Interest in CAT, XAT, NMAT, SNAP, and other Management Exams

Simple & Compound Interest and  carry high importance in management entrance exams like CAT, XAT, NMAT as compared to other management entrance exams to know more about the concepts in the topics and how to deal with the preparation with some previous year actual CAT questions please check below the details.

The Chapter on Interest forms an important topic from the CAT’s point of view. The use of the concepts of interest finds high importance in Quantitative aptitude and some questions of the data interpretation section. Prior understanding of percentages and percentage calculation is a must to study this chapter. The fast percentage calculation speed will help you in solving questions on interests each time. However, questions on interest are still important for exams like SNAP, NMAT, XAT, MAT, ATMA, CMAT, IRMA, and other management exams. Hence, if you are planning to go for all kinds of management exams- this chapter has high importance in mathematics too.

CAT :

 YEAR NO. OF QUESTIONS GOOD ATTEMPT DIFFICULTY LEVEL 2019 2 1 Moderate 2018 3 2 Moderate 2017 2 2 Easy

XAT :

 YEAR NO. OF QUESTIONS GOOD ATTEMPT DIFFICULTY LEVEL 2019 1 1 Easy 2018 1 1 Moderate 2017 2 1 Moderate

SNAP :

 YEAR NO. OF QUESTIONS GOOD ATTEMPT DIFFICULTY LEVEL 2019 3 2 Easy 2018 2 1 Moderate 2017 3 3 Easy

IIFT

 YEAR NO. OF QUESTIONS GOOD ATTEMPT DIFFICULTY LEVEL 2019 2 2 Easy 2018 2 1 Moderate 2017 3 3 Easy

NMAT
 YEAR NO. OF QUESTIONS GOOD ATTEMPT DIFFICULTY LEVEL 2020 2 2 Easy 2019 2 1 Moderate 2018 2 2 Moderate

### List of Concepts

Interest

Interest is the amount charged from the borrower by the lender on the principal loan sum. Interest is the cost of renting money and the rate at which interest is charged on the principal sum which is known as the interest rate. The interest rate charged depends on two factors:

1. The value of money does not remain the same over time. It changes with time. The net worth of ₹ 50 today will not be the same tomorrow i.e. If 5 pens could be bought presently with an INR 50 note then in the future, maybe only 4 pens can be bought with the same ₹ 50 note. The reason behind may be inflation or the hike in prices

2. The credibility of the borrower, if there is a chance of more risk and default on the borrower side then a high-interest rate is charged in the same way it will be lower if the risk factor is low and comparatively low default on the borrower side

The above two reasons become the basis of why interest rates are so relevant and important at the same time have a great effect on markets and the economy and forms an integral & important part of the curriculum in the MBA or PGDM programs. But, a relatively simpler level of questions is asked in the CAT, XAT, NMAT and other management exams based on the concepts learned at the time of high school.

These concepts are categorized into a type of interests

• Simple Interest
• Compound Interest

Let us first understand the concept of simple interest, It is a type of interest which once credited does not earn interest on itself and remains fixed over time.

The formula to calculate Simple Interest is

SI = {(P x R x T)/ 100}

Where

P = Principal Sum (the deposited amount or original loan)

R = rate of interest (the rate at which loan is charged)

T = Time period (the duration for which money is borrowed or deposited)

So, If the amount of P is borrowed at the rate of interest R for the period of T years then the amount to be repaid to the lender will be given by

A = P + SI

Some useful results on Simple Interest

Suppose If rate to interest is r1% for T1 years, r2% for T2 years …. rn for Tn years for investment and the Simple Interest obtained is ₹x on the investment. Then the principal amount is given by
x * 100/ (r1T1 + r2T2 + …+ rnTn)

If a person deposits a sum of ₹X at r1% p.a. and the sum of ₹Y at r2% p.a. then the rate of interest for the sum deposited is given by
R = {(Xr1 + Yr2)/ (X + 1)}

If a certain sum of money becomes “a” time in “T years” at Simple Interest, then the rate of interest p.a. is
R = 100(a – 1) / T

Suppose a certain amount  of money is lent out in n parts in such a way that an equal sum of money is available at simple interest on each part at the given interest rates at R1, R2, …, Rn respectively, and periods are mentioned as  T1, T2, …, Tn respectively, then the ratio in which the sum that will be divided into n parts is given by
1/R1T1: 1/R2T2….:1/RnTn

### Previous year questions

Q1.) A person invested a total amount of Rs 15 lakh. A part of it was invested in a fixed deposit earning 6% annual interest, and the remaining amount was invested in two other deposits in the ratio 2: 1, earning annual interest at the rates of 4% and 3%, respectively. If the total annual interest income is Rs 76000 then the amount (in Rs lakh) invested in the fixed deposit was _______? [CAT2019 Slot 1]

Final interest at the end of the year = 76000

Interest rate = 76000/1500000 *100 = 76/15 = 5 1/15

Combine interest rate from amount deposited at 4% and 3% interest rate = (4*2 + 3)/ (2+1) =11/3 % Let the amount ratio of amount deposited in fixed deposit and other deposit be x:y

so, x/y = (76/15 -11/3)/ (6 – 76/15)

x/y = (76-55)/ (90 -76) = 19:14

Q2.) Amount deposited in 6% = 19/33 *15 =8.63 lakh = 9 lakhQ2Amal invests Rs 12000 at 8% interest, compounded annually, and Rs 10000 at 6% interest, compounded semi-annually, both investments being for one year. Bimal invests his money at 7.5% simple interest for one year. If Amal and Bimal get the same amount of interest, then the amount, in Rupees, invested by Bimal is ______? [CAT2019 Slot 1]

Total amount invested by Amal = 12000(1+0.08) + 10000(1+0.06/2) ^2 = 12960+ 10609 = 23569

Bimal invests p amount at SI.

So, interest for Bimal = p*7.5*1/100 Interest are same for a and b,

so, we get 23569-22000 = p*7.5*1/100 So, p = 20920

Q3.) John borrowed Rs. 2,10,000 from a bank at an interest rate of 10% per annum, compounded annually. The loan was repaid in two equal instalments, the first after one year and the second after another year. The first instalment was the interest of one year plus part of the principal amount, while the second was the rest of the principal amount plus due interest thereon. Then each instalment, in Rs., is__________? [CAT2018 Slot 1]

Let each instalment be ₹x. Equating the present value of both the instalments to the money borrowed,

x/1.1   x/1.1^2   210000

x=121000

Q4.) Gopal borrows Rs. X from Ankit at 8% annual interest. He then adds Rs. Y of his own money and lends Rs. X+Y to Ishan at 10% annual interest. At the end of the year, after returning Ankit’s dues, the net interest retained by Gopal is the same as that accrued to Ankit. On the other hand, had Gopal lent Rs. X+2Y to Ishan at 10%, then the net interest retained by him would have increased by Rs. 150. If all interests are compounded annually, then find the value of X + Y? [CAT2018 Slot 2]

Interest to be repaid to Ankit at the end of the year = 0.08X

Interest that Gopal would receive from Ishan in two cases is as given.

Case I: if he lends X + Y

Interest received = (X + Y) × 0.1 = 0.1X + 0.1Y

Interest retained by Gopal after paying to Ankit = (0.1X + 0.1Y) – (0.08X) = 0.02X + 0.1Y

Given that Interest retained by Gopal is same as that accrued by Ankit => (0.02X + 0.1Y) = 0.08X

=> Y = 0.6X

Case II: if he lends X + 2Y

Interest received = (X + 2Y) × 0.1 = 0.1X + 0.2Y

Interest retained by Gopal after paying to Ankit = (0.1X + 0.2Y) – (0.08X) = 0.02X + 0.2Y

Given that interest retained by Gopal would increase by 150 => (0.02X + 0.2Y) – (0.02X + 0.1Y) = 150 0.1Y = 150 => Y = 1500 and X = 1500×0.6= 2500 Hence X + Y = 2500 + 1500 = 4000

### Preparation Phase for Interest

Interest form the important part of Arithmetic which has good contribution in the Quants section of CAT, XAT, SNAP, NMAT and other various management entrance exams We will divide the preparation of this topic into three phases following which can help the aspirants to score exceptionally well in the management entrance exams.

Phase I: In Phase I the candidate can start with basic concept understanding and should try solving the basic questions from the topics Interest. For this aspirant can follow Arun Sharma on Quantitative aptitude and after following the concept can solve the questions under Level of Difficulty 1 from the topic.

Phase II: In Phase II aspirants can start practicing questions from Level of difficulty 2 questions from Arun Sharma from the given topic Interest and also practice through the sectional test as time-based practice and analysis of the test is also necessary by this time.

Phase III: In Phase III aspirants can practice these topics from previous year papers of prominent management entrance exams like CAT, XAT, SNAP, NMAT, and various other exams. Aspirants can also practice through a mock test and analyse it thoroughly. Also, in this phase aspirant should go through the concepts once again at the same time should try solving advanced problems from the Interest and Linear equations.