# CAT Simple and Compound Interest Questions (with Notes) PDF

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Simple and Compound Interest is one of the key topics in the CAT Quants (Arithmetic) section. Over the past few years, CAT CI and SI questions have made a recurrent appearance in the Quants section. You can expect around 1-2 questions in the 22-question format of the CAT Quant section. You can check out these  CAT Simple & Compound Interest Questions from Previous years. In this article, we will look into some important CAT Simple and Compound Interest Questions (with Notes) PDF. These are a good source for practice; If you want to practice these questions, you can download these CAT SI & CI Questions PDF, which is completely Free.

• CAT Simple and Compound Interest – Tip 1: A few CAT CI & SI questions appear in the CAT and other MBA entrance exams every year. If you’re starting the prep, firstly understand the CAT Arithmetic Syllabus; Based on our analysis of the previous years CAT questions,  this was the CI & SI weightage in CAT: 1-2 questions were asked on this topic (in CAT 2021).
• CAT Simple and Compound Interest – Tip 2: Be thorough with all the basics of this topic. CAT Simple and Compound Interest is an easy topic, and hence must not be avoided. Practice these CAT questions on Simple and Compound Interest PDF, with Video solutions. Learn all the major formulae from these concepts. You can check out the Important Simple and Compound Interest for CAT Formulas PDF here.

Question 1: A sum of money compounded annually becomes Rs.625 in two years and Rs.675 in three years. The rate of interest per annum is

a) 7%

b) 8%

c) 6%

d) 5%

Solution:

As we know, formulae of compound interest for 2 years  will be:
$P(1+\frac{r}{100})^{2}$ = 625  (Where r is rate, P is principal amount)
For 3 years:
$P(1+\frac{r}{100})^{3}$ = 675
Dividing above two equations we will get r=8%

Question 2: 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

Solution:

We have to equate the installments and the amount due either at the time of borrowing or at the time when the entire loan is repaid. Let us bring all values to the time frame in which all the dues get settled, i.e, by the end of 2 years.

John borrowed Rs. 2,10,000 from the bank at 10% per annum. This loan will amount to 2,10,000*1.1*1.1 = Rs.2,54,100 by the end of 2 years.
Let the amount paid as installment every year be Rs.x.

John would pay the first installment by the end of the first year. Therefore, we have to calculate the interest on this amount from the end of the first year to the end of the second year. The loan will get settled the moment the second installment is paid.

=> 1.1x + x = 2,54,100
2.1x = 2,54,100
=> x = Rs. 1,21,000.

Therefore, 121000 is the correct answer.

Question 3: 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.

Solution:

Amount of interest paid by Ishan to Gopal if the borrowed amount is Rs. (X+Y) = $\dfrac{10}{100}*(X+Y)$ = 0.1(X+Y)

Gopal also borrowed Rs. X from Ankit at 8% per annum. Therefore, he has to return Ankit Rs. 0.08X as the interest amount on borrowed sum.

Hence, the interest retained by gopal = 0.1(X+Y) – 0.08X = 0.02X + 0.1Y   … (1)

It is given that the net interest retained by Gopal is the same as that accrued to Ankit.

Therefore, 0.08X = 0.02X + 0.1Y

$\Rightarrow$ X = (5/3)Y   … (2)

Amount of interest paid by Ishan to Gopal if the borrowed amount is Rs. (X+2Y) = $\dfrac{10}{100}*(X+2Y)$ = 0.1X+0.2Y

In this case the amount of interest retained by Gopal = 0.1X+0.2Y – 0.08X = 0.02X + 0.2Y   … (3)

It is given that the interest retained by Gopal increased by Rs. 150 in the second case.

$\Rightarrow$ (0.02X + 0.2Y) – (0.02X + 0.1Y) = 150

$\Rightarrow$ Y = Rs. 1500

By substituting value of Y in equation (2), we can say that X = Rs. 2500

Therefore, (X+Y) = Rs. 4000.

Question 4: 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

Solution:

The amount with Amal at the end of 1 year = 12000*1.08+10000*1.03*1.03=23569

Interest received by Amal = 23569-22000=1569

Let the amount invested by Bimal = 100b

Interest received by Bimal = 100b*7.5*1/100=7.5b

It is given that the amount of interest received by both of them is the same

7.5b=1569

b=209.2

Amount invested by Bimal = 100b = 20920

Question 5: 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

Solution:

Assuming the amount invested in the ratio 2:1 was 200x and 100x, then the fixed deposit investment = 1500000-300x

Hence, the interest = 200x*4/100 = 8x and 100x*3/100=3x

Interest from the fixed deposit = (1500000-300x)*6/100 = 90000-18x

Hence the total interest  = 90000-18x+8x+3x=90000-7x =76000

=> 7x=14000   => x=2000

Hence, the fixed deposit investment = 1500000-300*2000 = 900000 = 9 lakhs

Question 6: Veeru 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?

Solution:

Let their individual Amounts be equal after ‘t’ years. Let their initial investments amount to $A_V$ and $A_J$ ;

$A_V\ =10,000\left(1+\frac{5t}{100}\right)$ and $A_J\ =8,000\left(1+\frac{10\left(t-2\right)}{100}\right)$

Equating both: $10,000\left(1+\frac{5t}{100}\right)\ =8,000\left(1+\frac{10\left(t-2\right)}{100}\right)$

On simplifying both sides, we get: $15t\ =\ 180\ ;\ t\ =\ 12$

Question 7: A person invested a certain amount of money at 10% annual interest, compounded half-yearly. After one and a half years, the interest and principal together became Rs.18522. The amount, in rupees, that the person had invested is

Solution:

Given,

Rate of interest = 10%

Since it is compounded half-yearly, R=5%

n=3

We know, A = $P\left(1+\frac{R}{100}\right)^{^n}$

18522 = $P\left(1+0.05\right)^3$

=> P = 16000

Question 8: 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

Solution:

For two years the compound interest is $\frac{PR(1)}{100}+\frac{PR(1)}{100}\left(1+\frac{PR(1)}{100}\right)$

For three years the simple interest is $\frac{9PR}{100}$

Now R(1)= 5% and R=3%

Hence $\frac{5P}{100}+\frac{5P}{100}\left(1.05\right)-\frac{9P}{100}=1125$

$\frac{-4P}{100}+\frac{5.25P}{100}=1125$

$\frac{1.25P}{100}=1125$

Solving we get P= 90000

Question 9: Anil invests some money at a fixed rate of interest, compounded annually. If the interests accrued during the second and third year are ₹ 806.25 and ₹ 866.72, respectively, the interest accrued, in INR, during the fourth year is nearest to

a) 929.48

b) 934.65

c) 931.72

d) 926.84

Solution:

Let the principal amount be P and the interest rate be r.

Then $P\left(1+r\right)^2-P\left(1+r\right)=806.25$ -(1)

$P\left(1+r\right)^3-P\left(1+r\right)^2=866.72$ -(2)

Dividing (2) by (1), we get:

$\frac{\left(P\left(1+r\right)^3-P\left(1+r\right)^2\right)}{P\left(1+r\right)^2-P\left(1+r\right)}=\frac{866.72}{806.25}$

$\frac{\left(\left(1+r\right)^2-1-r\right)}{1+r-1}=1.075$

$\frac{r^2+r}{r}=1.075$

r=0.075 or 7.5%

$\frac{\left(Interest\ accrued\ in\ 4th\ yr\right)}{Interest\ accrued\ in\ 3rd\ yr}=\frac{X}{866.72}$

$\frac{\left(P\left(1+r\right)^4-P\left(1+r\right)^3\right)}{P\left(1+r\right)^3-P\left(1+r\right)^2}=\frac{X}{866.72}$

Dividing numerator and denominator by $P\left(1+r\right)^2$

$\frac{r^2+2r+1-1-r}{1+r-1}=\frac{X}{866.72}$

$r+1=\frac{X}{866.72}$

$X=1.075\times\ 866.72=931.72$

Question 10: Bank A offers 6% interest rate per annum compounded half-yearly. Bank B and Bank C offer simple interest but the annual interest rate offered by Bank C is twice that of Bank B. Raju invests a certain amount in Bank B for a certain period and Rupa invests ₹ 10,000 in Bank C for twice that period. The interest that would accrue to Raju during that period is equal to the interest that would have accrued had he invested the same amount in Bank A for one year. The interest accrued, in INR, to Rupa is

a) 3436

b) 2436

c) 2346

d) 1436

Solution:

Bank A: 6% p.a. 1/2 yearly (CI)

Bank B: x% p.a (SI)

Bank C: 2x% p.a (SI)

Let Raju invest Rs P in bank B for t years. Hence, Rupa invests Rs 10,000 in bank C for 2t years.

Now,

$P\left(\frac{x}{100}\right)t\ =\ P\left(1+\frac{3}{100}\right)^2-P$

$\left(\frac{x}{100}\right)t\ =\ 1.0609-1$

$\left(\frac{x}{100}\right)t\ =\ 0.0609$

We need to calculate

SI = $10000\times\ 2t\times\ \left(\frac{2x}{100}\right)=40000\left(\frac{x}{100}\right)t=40000\times\ 0.0609=2436$

Instructions

Directions for the following two questions: Shabnam is considering three alternatives to invest her surplus cash for a week. She wishes to guarantee maximum returns on her investment. She has three options, each of which can be utilized fully or partially in conjunction with others.

Option A: Invest in a public sector bank. It promises a return of +0.10%.

Option B: Invest in mutual funds of ABC Ltd. A rise in the stock market will result in a return of +5%, while a fall will entail a return of – 3%.

Option C: Invest in mutual funds of CBA Ltd. A rise in the stock market will result in a return of – 2.5%, while a fall will entail a return of + 2%.

a) 0.25%

b) 0.10%

c) 0.20%

d) 0.15%

e) 0.30%

Solution:

Let a, b and c be the percentages of amount invested in options A, B and C respectively => a + b + c = 100

Return attained if there is a rise in the stock market => 0.001a + 0.05b – 0.025c

Return attained if there is a fall in the stock market => 0.001a – 0.03b + 0.02c

Maximum guaranteed return is attained when both are equal because it is indifferent to rise and fall in the market.

0.001a + 0.05b – 0.025c = 0.001a – 0.03b + 0.02c

=> 0.08b = 0.045c => 16b = 9c

Let’s put the values for a, b and c that satisfy the above equation.

b = 9, c = 16, a = 75 => return = 0.125

b = 18, c = 32, a = 50 => return = 0.15

b = 27, c = 48, a = 25 => return = 0.175

b = 36, c = 64, a = 0 => return = 0.2

Hence, the maximum guaranteed return is 0.2%

a) 100% in option A

b) 36% in option B and 64% in option C

c) 64% in option B and 36% in option C

d) 1/3 in each of the three options

e) 30% in option A, 32% in option B and 38% in option C

Solution:

Let a, b and c be the percentages of amount invested in options A, B and C respectively => a + b + c = 100

Return attained if there is a rise in the stock market => 0.001a + 0.05b – 0.025c

Return attained if there is a fall in the stock market => 0.001a – 0.03b + 0.02c

Maximum guaranteed return is attained when both are equal because it is indifferent to rise and fall in the market.

0.001a + 0.05b – 0.025c = 0.001a – 0.03b + 0.02c

=> 0.08b = 0.045c => 16b = 9c

Let’s put the values for a, b and c that satisfy the above equation.

b = 9, c = 16, a = 75 => return = 0.125

b = 18, c = 32, a = 50 => return = 0.15

b = 27, c = 48, a = 25 => return = 0.175

b = 36, c = 64, a = 0 => return = 0.2

Hence, the maximum guaranteed return is 0.2% and it is attained when 36% is invested in option B and 64% is invested in option C.