Simple Interest and Compound Interest CAT Questions and answers

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Question 1: Some amount was lent at 10% p.a Simple Interest. After 1 year, Rs 4400 is repaid and the rest of the amount is repaid at 20% p.a. If the 2nd year’s interest is 11/7 of the first year’s interest, find the amount of money that was lent out initially ?

a) Rs.12000
b) Rs.13000
c) Rs.14000
d) Rs.15000

Question 2: Ramesh takes a loan of Rs 20000 from Karan at a simple interest of 20%. He agrees to clear the loan, along with the interest, in four equal installments, each at the end of one year, for four years. But, Karan puts forward a condition that he will continue to calculate the interest on the original amount lended till Ramesh completely pays off his loan. What is the value of each installment?

a) Rs 9000
b) Rs 9500
c) Rs 10000
d) None of these

Question 3: Mohan borrowed 10000 rupees from Sohan. Sohan charges a simple interest of 10 pa. Mohan returned 4000 Rs after 1year which included the interest for the first year. He returned the remaining amount after 2 more years. What is the interest that Mohan ended up paying?

a) 2000
b) 2400
c) 2500
d) 3000

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Question 4: Ravi invests a sum of money in a bank which gives a simple interest of 5% p.a. He invests twice the amount of money in another bank which gives a interest of 3% pa compounded annually. At the end of 3 years the interest earned from which bank would be higher and by what percent(approx)?

a) 1st, 25%
b) 2nd, 10%
c) 2nd, 24%
d) 1st. 15%

Question 5: Rahul takes a loan of Rs 150000 at an interest rate of 20% compound interest, which is compounded annually. He agrees to pay three equal installments in three years, one installment at the end of every year. Find the value of each installment.

a) Rs 71209
b) Rs 68349
c) Rs 76484
d) Rs 72904

Solutions for Simple Interest Compound Interest CAT Questions:

Solutions:

1) Answer (C)

Let the amount be x.
After 1 year the amount becomes 1.1x out of which 4400 is repaid.
Interest for second year = 20% of (1.1x-4400)
(1.1x-4400)/5 = 11/7 (1.1x-x)
7.7x-30800 = 55(0.1x)
2.2x = 30800
x = 14000
Rs 14000 was lent initially

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2) Answer (A)

The loan is taken for simple interest => Interest is always calculated on the initial principal amount and not on the outstanding amount.
=> The interest for each of the four years is the same, which is equal to $\frac{20000*20*1}{100}$ = Rs 4000.
Interest for four years = 4 * 4000 = Rs 16000.
Total amount = 20000 + 16000 = Rs 36000
=> Each equal installment = $\frac{36000}{4}$ = Rs 9000

3) Answer (B)

Principal for first year = 10000, So interest for first year would be 10000*10/100 = 1000
Now for the remaining two years, the principal would be 7000, so interest that he will pay in 2 years = 7000*2*10/100 = 1400
Thus, the total interest that he ends up paying is 1400 + 1000 = 2400

4) Answer (C)

Let the amount invested in first bank be x
So interest earned in 3 years = x*5*3/100 = .15x
Now amount invested in second scheme is 2x
So the amount after 3 years would be
$(1.03)^{3}*2x$ = 2.185x
So the interest earned = .185x
Thus the interest earned in second case is 24% more than the interest earned in first case.

5) Answer (A)

Let the installment paid be x.
The amount 150000 earns an interest for 3 years. So, the installments must also compensate for the interest.
The first installment paid will earn an interest for 2 more years, the second installment paid will earn an interest for 1 more year and the last installment paid will earn not earn any interest.
=> $150000(1.2)^3 = x(1.2)^2 + x(1.2) + x$
=> $150000(1.2)^3 = 3.64x$
=> x = Rs 71209

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