 # CAT Questions | CAT Arithmetic Questions: Simple and Compound Interest

### CAT Verbal Ability

Simple & Compound Interest and carry high importance in management entrance exams like CAT, XAT, NMAT. It is an integral part of the Arithmetic chapter, and it also holds great relevance in other sections like Data Interpretation in these entrance exams. 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. Students can expect at least 1-3 questions from Simple and Compound Interest. Hence, if you are planning to go for all kinds of management exams – Simple and Compound Interest chapter has high importance in mathematics too.

## CAT Quantitative Aptitude questions | CAT Arithmetic: Simple and Compound Interest

Below you will find Simple Interest questions and questions on Compound Interest that came in previous years’ CAT papers.

### Q.1 : Veera invested Rs 10000 at 5% simple annual interest, and exactly after two years, Joy invested Rs 8000 at 10% simple annual interest. How many years after Veeru’s investment, will their balances, i.e., principal plus accumulated interest, be equal? ____________ [CAT 2020]

Let assume its equal after N years

Veeru’s investment after N years = 10000 + 10000 × (5/100) × N

Joy’s investment after N years = 8000 + 8000 × (10/100) × (N – 2)

Equating both

10000 + 10000 × (5/100) × N = 8000 + 8000 × (10/100) ×(N – 2)

10000 + 500N = 8000 + 800N – 1600

3600 = 300N

N = 12

### Q.2: For the same principal amount, the compound interest for two years at 5% per annum exceeds the simple interest for three years at 3% per annum by Rs. 1125.Then the principal amount in rupees is _____________ [CAT 2020]

P (1.05) 2 – P = CI
P × 3 × 3/100 = SI
CI = 0.1025 P
SI = 0.09 P
CI – SI = 0.0125 P = 125/10000 P = 1125
P = 90000

### Q.3: Amal 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 _____________ [CAT 2019]

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

### Q.4: 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 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 ____________ [CAT 2018]

Let each instalment be ₹x. Equating the present value of both the instalments to the money borrowed,
(x/1.1) + (x/1.12) = 210000
x = 121000

## Basic Concepts in Simple and Compound Interest:

### 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 for Simple Interest sums

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

## Preparation Phase for Simple and Compound Interest

Simple Interest and Compound Interest questions forms 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 simple interest and compound interest problems. For this aspirant can follow MBAP CAT E-book (Concept Theory) study material and after following the concept, they can solve the questions under Level of Difficulty 1 from the topic.

### Phase II:

In Phase II aspirants can start practicing problems on simple interest and compound interest from Level of difficulty 2 questions. They can use MBAP Live Lecture Recording (Basic) for understanding the basic concepts and also practice through the sectional test as time-based practice and analysis of the test is also necessary by this time. Following this is very necessary to have a strong hold on Simple and Compound Interest topic.

### Phase III:

In Phase III aspirants can practice interest questions from previous year papers of prominent management entrance exams like CAT, XAT, SNAP, NMAT, and use MBAP CAT E-book (Practice Questions). Aspirants can also practice through a mock test and analyze it thoroughly. Also, in this phase aspirants should use MBAP lecture assignments for practice and also go through the concepts once again at the same time should try solving advanced problems from Simple and Compound Interest and Linear equations. Counselling Session
By IIM Mentor

#### Words From Our Students Nihar Mehta
Calls from IIMs, SPJIMR & MDI
During my CAT preparation, I enrolled at MBA Pathshala for classroom coaching. Abhijit Sir & Haider Sir guided me through the process of planning & executing the strategies I had to use to succeed in the test. I received regular feedback on my progress during the GD and PI preparations after CAT. I received calls from IIMs, SPJIMR, and MDI. MBAP played a huge role in this, and I cannot thank them enough for their efforts. Ishan Rathod
Calls from IIM I, S, and all New And Baby IIM's.
MBAP is a great place to prepare for MBA-CET, CAT, and CMAT, and the faculty are unbeatable. Most importantly, they pay personal attention to each student. Most faculty members come from IIMs. One-on-one interaction helped me improve as the exams approached, as well as get calls from IIMs I, S, and all New and Baby IIMs. Interview sessions were very beneficial for me to convert IIM S. Sanskriti Reja
Calls from IIMs, XLRI, XIMB
I am glad I chose MBA Pathshala for my MBA coaching. The faculty here is excellent and very competent. If I had any questions or needed extra classes, they always gave me one. I got through my GD-PIs too after the exams with their help. Thanks to MBAP, I was able to pass CAT and other entrance exams. Among others, I received calls from XLRI, XIMB, and IIMs. A few of the colleges I've converted are KJ Somaiya, TAPMI, IIM Sambalpur, and IIM Sirmaur. Parth Kanakia
Converted SPJIMR
MBAP prepared me for GD, WAT, and PI. Abhijit Singh, Haider, and other MBAP faculty provided excellent training. Good knowledge was imparted from the very beginning. Regular mock interviews were conducted. As a former SPJIMR, I would recommend students to join MBAP. Ronit jaiswal
Calls from IIM-A/B/C & SNAP 98.12%ile
Coaching offers me personalized attention and a competitive environment. Because the preparation was so rigorous, I eventually began to perform at my best. The mock interviews/GD/WATs were conducted by anonymous panels, and it really boosted my confidence. Although I got a call from SCMHRD (SNAP-98.12), Abhijeet sir felt that I should try again and aim for IIM-A/B/C. It has been your pleasure to have been your mentor. Maitreya Khanapurkar
Calls From IIMs
You will get good support from the faculty until you get into a B-School. The shortcut techniques you will learn will be extremely useful. You will be able to resolve doubts at any time. If you plan on taking CAT CET or any other entrance exam, go for MBA Pathshala. With the help of MBAP tutors, I received a call from IMT Ghaziabad.
Yash Dandavate
GMAT Score - 660
GMAT prep with MBAP was the best I've ever experienced. With Rohan Kulkarni Sir's Verbal Guidance, I scored 85th percentile in my GMAT exam as I was very weak in English. I always found Haider Sir and Abhijeet to answer my questions and to develop strategies and shortcuts to tackle GMAT problems for me. MBAP is a great option for GMAT and CAT prep.

#### Free Material Area  