CAT Simple Interest Compound Interest Questions & Solutions

A sample of real CAT Simple Interest Compound Interest past-year questions, each with a worked solution and the correct answer highlighted. AthenaPrep has 21 Simple Interest Compound Interest questions in all — sign up free to practise them timed.

1. Q1.CAT 2025

   At a certain simple rate of interest, a given sum amounts to Rs 13920 in 3 years, and to Rs 18960 in 6 years and 6 months. If the same given sum had been invested for 2 years at the same rate as before but with interest compounded every 6 months, then the total interest earned, in rupees, would have been nearest to

   • 3221

   • 3180

   • 3150

   • 3096

   Show solution

   Let the principal be ₹ P and rate of interest be r%.

   Now,  $13920=P+\dfrac{P\times\ r\times\ 3}{100}$

   or,  $13920-P=\dfrac{P\times\ r\times\ 3}{100}$ ---->(1)

   Also,  $18960=P+\dfrac{P\times\ r\times\ 13}{100\times\ 2}$

   $18960-P=\dfrac{P\times\ r\times13}{100\times\ 2}$ ----->(2)

   Dividing eqn(1) by eqn(2),

   $\dfrac{13920-P}{18960-P}=\dfrac{3}{\frac{12}{2}}=\dfrac{6}{13}$

   or,  $\left(13920-P\right)13=\left(18960-P\right)6$

   or,  $13920\times\ 13-13P=18960\times\ 6-6P$

   or,  $13920\times\ 13-18960\times\ 6=13P-6P$

   or, $180960-113760=7P$

   or,  $67200=7P$

   or,  $P=\dfrac{67200}{7}=9600$

   Putting this in equation (1),

   $13920-9600=\dfrac{9600\times\ r\times\ 3}{100}$

   or,  $4320=96\times\ 3r$

   or,  $r=\dfrac{4320}{96\times\ 3}=15$

   So, rate percent is $15\%$

   Now if the same sum had been invested for 2 years at the same rate as before but with interest compounded every 6 months, amount =  $9600\left(1+\dfrac{\frac{15}{2}}{100}\right)^4=9600\left(1+\frac{7.5}{100}\right)^4$

   So, interest =  $9600\left(1+\frac{7.5}{100}\right)^4-9600$

   = Rs 3220.50

   = Rs 3221

   So, the total interest earned is Rs 3221.

2. Q2.CAT 2025

   Kamala divided her investment of Rs 100000 between stocks, bonds, and gold. Her investment in bonds was 25% of her investment in gold. With annual returns of 10%, 6%, 8% on stocks, bonds, and gold, respectively, she gained a total amount of Rs 8200 in one year. The amount, in rupees, that she gained from the bonds, was

   Answer: 900

   Show solution

   Let the amounts invested in Stocks be S, Bonds B, and, Gold be G

   Given that   $S + B + G = 100000, B = 0.25G$
   

   $0.10S + 0.06B + 0.08G = 8200$
   

   Substitute S = 100000 - B - G = 100000 - 1.25G

     $0.10(100000 - 1.25G) + 0.06(0.25G) + 0.08G = 8200$

   $10000 - 0.125G + 0.015G + 0.08G = 8200$

   $10000 - 0.03G = 8200$

   $0.03G = 1800 \Rightarrow G = 60000$

   $B = 0.25G = 15000$
   

   Gain from bonds = $0.06 \times 15000 = 900$
   

3. Q3.CAT 2024

   Anil invests Rs 22000 for 6 years in a scheme with 4% interest per annum, compounded half-yearly. Separately, Sunil invests a certain amount in the same scheme for 5 years, and then reinvests the entire amount he receives at the end of 5 years, for one year at 10% simple interest. If the amounts received by both at the end of 6 years are equal, then the initial investment, in rupees, made by Sunil is

   • 20860

   • 20640

   • 20480

   • 20808

   Show solution

   Let's take the amount invested by Sunil to be X. 

   The amount received by Anil at the end of 6 years would be  $22000\left(1+\frac{4}{2\times\ 100}\right)^{6\times\ 2}=22000\left(1.02\right)^{12}$

   The amount received by Sunil at the end of 5 years would be  $X\left(1.02\right)^{10}$
   In the 6th year, Sunil invests this at a simple interest of 10%, giving him an interest of  $X\left(1.02\right)^{10}\times\ 0.1$
   Giving the total amount with him at the end of 6 years to be  $X\left(1.02\right)^{10}\times\ \left(1+0.1\right)$

   Equating the final amount with Sunil and Anil, we get:
   $X\left(1.02\right)^{10}\times\ \left(1.1\right)=22000\left(1.02\right)^{12}$
   $X=\frac{22000\left(1.02\right)^2}{1.1}=20808$

   Therefore, Option D is the correct answer. 

4. Q4.CAT 2024

   Aman invests Rs 4000 in a bank at a certain rate of interest, compounded annually. If the ratio of the value of the investment after 3 years to the value of the investment after 5 years is 25 : 36, then the minimum number of years required for the value of the investment to exceed Rs 20000 is

   Answer: 9

   Show solution

   Let us assume the amount invested to be $P$ , and the rate of interest to be $r$ . 
   Value of the investment after 3 years will be,  $P\left(1+r\right)^3$
   Value of the investment after 5 years will be,  $P\left(1+r\right)^5$

   $\left(1+r\right)^2=\frac{36}{25}$
   $\left(1+r\right)^2=1.44$
   $r=0.2$
   

   We need to find the value of n for which  4000\left(1+r\right)^n>20000
   \left(1+r\right)^n>5
   \left(1.2\right)^n>5
   We see that, 
   $1.2^8=4.2999$
   $1.2^9=5.15$

   Hence it takes 9 years to grow to over 20,000. 

5. Q5.CAT 2023

   Anil borrows Rs 2 lakhs at an interest rate of 8% per annum, compounded half-yearly. He repays Rs 10320 at the end of the first year and closes the loan by paying the outstanding amount at the end of the third year. Then, the total interest, in rupees, paid over the three years is nearest to

   • 45311

   • 51311

   • 33130

   • 40991

   Show solution

   It is given that Anil borrows Rs 2 lakhs at an interest rate of 8% per annum, compounded half-yearly. It is also known that he repays Rs 10320 at the end of the first year and closes the loan by paying the outstanding amount at the end of the third year.

   The total amount at the end of the first year is:  $200000\times\ \frac{104}{100}\times\ \frac{104}{100}=216320$

   He repays 10320 rupees at the end of the first year, which implies the amount that remains unpaid at the end of the first year is 206000 rupees.

   This unpaid amount will accrue interest for another two years.

   Hence, the final amount at the end of three years is  $206000\times\ \frac{104}{100}\times\ \frac{104}{100}\times\ \frac{104}{100}\times\ \frac{104}{100}=240990.86$

   Hence, the accrued interest in these two years is (240990.86-206000) = 34990.86 rupees.

   Hence, the total interest accrued over the three years = (34990.86+16320) = 51311 rupees.

   The correct option is B

6. Q6.CAT 2022

   Alex invested his savings in two parts. The simple interest earned on the first part at 15% per annum for 4 years is the same as the simple interest earned on the second part at 12% per annum for 3 years. Then, the percentage of his savings invested in the first part is

   • 37.5%

   • 62.5%

   • 60%

   • 40%

   Show solution

   Let the savings invested in first part and second part be 'x' and 'y', respectively.

   It is given,

   $\ \frac{\ x\times15\times4}{100}=\ \frac{\ y\times12\times3}{100}$

   60x = 36y

   5x = 3y

   Required percentage =  $\frac{x}{x+y}\times100=\frac{3}{3+5}\times100=37.5\%$

   The answer is option A.

7. Q7.CAT 2022

   Nitu has an initial capital of ₹20,000. Out of this, she invests ₹8,000 at 5.5% in bank A, ₹5,000 at 5.6% in bank B and the remaining amount at x% in bank C, each rate being simple interest per annum. Her combined annual interest income from these investments is equal to 5% of the initial capital. If she had invested her entire initial capital in bank C alone, then her annual interest income, in rupees, would have been

   • 700

   • 800

   • 900

   • 1000

   Show solution

   It is given,

   $\ \frac{\ 5.5\times1\times8000}{100}+\ \frac{\ 5.6\times1\times5000}{100}+\ \frac{\ x\times1\times7000}{100}=\frac{5}{100}\times20000$

   $440+280+70x=1000$

   x = 4%

   Interest =  $\ \frac{\ 20000\times4\times1}{100}$ = Rs 800

   The answer is option B.

8. Q8.CAT 2021

   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

   • 3436

   • 2436

   • 2346

   • 1436

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

9. Q9.CAT 2020

   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

   Answer: 16000

   Show 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

10. Q10.CAT 2020

    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

    Answer: 90000

    Show 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

11. Q11.CAT 2019

    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

    Answer: 9

    Show 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

12. Q12.CAT 2018

    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.

    Answer: 4000

    Show 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.

CAT Simple Interest Compound Interest previous year questions with solutions — AthenaPrep