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CAT Questions | CAT Arithmetic Questions: Simple and Compound Interest

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]

Answer:

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]

Answer:

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]

Answer:

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]

Answer:

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.

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