CAT 2020 Slot 3 Question 1- 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
Explanation
A 10% annual interest is a 5% bi-annual interest.
Hence interst for half an year is 5%.
The Principal, P is invested for 1.5 years or 3 terms of half years.
Therefore, P (1 + 5%)3 = 18522
P(1.05)3 = 18522
P × 21/20 × 21/20 × 21/20 = 18522
P × 7/20× 7/20 × 7/20= 686
P × 1/20 × 1/20 × 1/20 = 2
P = 2 × 20 × 20 × 20 = 16000.
CAT 2020 Slot 2 Question 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
Explanation
P(1.05)2 – P = CI
P × 3 × 3/100 = SI
CI = 0.1025 P
SI = 0.09P
CI – SI = 0.0125P = 125/10000
P = 1125
P = 90000
CAT 2020 Slot 1 Question 3- 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?
Explanation
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
CAT 2019 Slot 2 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
Explanation
The amount on the first investment of Anmol = 12,000 * (1.08) = 12,960
So the Interest on this investment is 12,960 – 12,000 = 960.
The amount on the second investment of Anmol = 10,000 * (1.03)2 = 10,609
So the Interest on this investment is 10,609 – 10,000 = 609.
So the total interest on these returns = 960 + 609 = 1,569.
Bimal has to get this as Simple Interst by investing X rupees at 7.5%
That means, X * 0.075 = 1,569
X = 20,920
So, Bimal has to invest 20,920 rupees.
CAT 2019 Slot 1 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
Explanation
Let Rs x be invested in FD.
So, Remaining amount = Rs. 15 Lakhs – x, which is invested in the ratio 2 : 1
So, each investment would have (15-x) and (15-x) investments respectively
So, Total annual interest income = 6% of x + 4% of (15-x) + 3% of (15-x) = 76000
Rewriting Rs. 76000 as Rs. 0.76 Lakhs,
6% of x + 4% of (15-x) + 3% of (15-x) = 0.76
Multiply both sides by 100,
6x + (15-x) + 2(15-x) = 76
6x + (15-x) = 76
165 + 18x -11x = 228
7x = 63
x = 9 (or) Rs. 9 Lakhs
CAT 2018 Slot 2 Question 6- 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.
Explanation
Gopal receives 10% of X + Y from Ishan as interest, from which he pays the interest of 8% of X to Ankit
So, Gopal would gain 2% of X + 10% of Y as interest and Ankit would gain 8% Interest
Its given that both the interest values are same, so 2% X + 10% Y = 8% X
3% X = 5% Y — (1)
Its also given that, if Gopal lend Rs. X + 2Y to Ishan at 10% interest, the net interest retained would increase by Rs. 150
So, the increase in 10% Y accounts for Rs. 150
10% Y = 150 => Y = Rs. 1500
Substituting the value in (1), we get 5 × 1500 = 3 × X => X = 2500
So, X + Y = 2500 + 1500 = Rs 4000
CAT 2018 Slot 1 Question 7- 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.
Explanation
Given, money borrowed = Rs. 2,10,000
At 10% Interest, after 1 year
Outstanding amount = Rs. 1.1 × 2,10,000 = Rs. 2,31,000
Let the First Installment be x
So, Due amount = Rs. 2,31,000 – x
This due amount is carried over to the second year, with an interest of 10%
So, Outstanding amount for Second year = Rs. 1.1 × (2,31,000 – x)
This amount will be payed as Second Installment
We know, Installment for year 1 = Installment for year 2 = Rs. x
1.1 × (2,31,000 – x) = x
2.1 x = 2,54,100
x = Rs. 1,21,000
CAT 2022 Slot 1 Question 8-
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
A.62.5%
B.37.5%
C.60%
D.40%
Explanation
Let ₹x be invested in the first instrument and ₹y be invested in the second instrument.
The interest earned in the first instrument = 0.15 * x * 4
The interest earned in the second instrument = 0.12 * y * 3
0.15 * x * 4 = 0.12 * y * 3
20 x = 12 y
x : y = 3 : 5
This means, 3/8th of the Savings was invested in the first instrument.
3/8
as a percentage is 37.5%
CAT 2022 Slot 2 Question 9- Mr. Pinto invests one-fifth of his capital at 6%, one-third at 10% and the remaining at 1%, each rate being simple interest per annum. Then, the minimum number of years required for the cumulative interest income from these investments to equal or exceed his initial capital is
Explanation
Let the capital invested by Mr.Pinto be ₹300.
₹300 because we deal with one-third, further in the question.
The interest generated is ₹15 per year.
Let’s say the capital is invested for n years.
When return equals capital…
15 n = 300
n = 20.
CAT 2022 Slot3 Question10- 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
A.900
B.700
C.1000
D.800
Explanation
If Neetu intended to get a 5% annual interest, ideally all the banks should have maintained a 5% interest rate.
But Bank A returns 0.5% extra interest on 8000 rupees, which is 40 rupees.
But Bank B returns 0.6% extra interest on 5000 rupees, which is 30 rupees.
A & B combines are paying 70 rupees extra than 5%.
So Bank C should maintain such an interest rate that, the interest generated on the remaining 7000 rupees is 70 less than 5% interest.
Since 70 is 1% of 7000. The interest rate at Bank C should be 5% – 1% = 4%
If all the 20,000 rupees were invested in Bank C, the interest generated is 4% of 20,000 = 800 rupees.
CAT 2021 Slot 1- Question 11- If Neetu intended to get a 5% annual interest, ideally all the banks should have maintained a 5% interest rate.
But Bank A returns 0.5% extra interest on 8000 rupees, which is 40 rupees.
But Bank B returns 0.6% extra interest on 5000 rupees, which is 30 rupees.
A & B combines are paying 70 rupees extra than 5%.
So Bank C should maintain such an interest rate that, the interest generated on the remaining 7000 rupees is 70 less than 5% interest.
Since 70 is 1% of 7000. The interest rate at Bank C should be 5% – 1% = 4%
If all the 20,000 rupees were invested in Bank C, the interest generated is 4% of 20,000 = 800 rupees.
Explanation
Here x is the rate of interest.
If you observe, the interest is in geometric progression(G.P).
In G.P, the common ratio =866.72/806.25
.
The interest in the fourth year = 866.72 x 866.72/806.25
≅931.72
CAT 2021 Slot-3 Question12- 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.2436
B.3436
C.2346
D.1436
Explanation
Bank A has a rate of interest of 6% and compounds half yearly.
This is the same as having a 3% interest rate per half-year.
So, if a Principal, P is invested for an year in bank A, at the end of the year it becomes P(1.03)(1.03) = P(1.0609)
Therefore the interest rate when viewed as a Simple interest scheme is 6.09% per annum.
Rupa invested in Bank C, which has twice the interest rate as Bank B and the quantum for which the investment is made is also double, hence Rupa effectively gets 4 times the interest that Raju gets for the same investment in Bank A.
Let’s say Raju invested ₹ 10,000 in Bank B.
Since this is the same as investing in Bank A for 1 year, his interest would be 6.09% of 10,000 = ₹ 609.
Now, for the same investment, Rupa must earn 4 times that of ₹ 609
So, Rupa earns ₹ 2,436
