# CAT Questions on Installments

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CAT Questions on Installments:

Installments is one of the applications profit, loss and discount. In previous years in CAT exam, many times, the questions were being asked on Installments. So, we have provided some problems with solutions on Installments for CAT. This serves as a good practice set for CAT Exam preparation related to profit and loss topic.

Question 1: 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

Question 2: A customer goes to a shop to purchase a car for Rs. 50,0000. The shopkeeper follows the following scheme. He offers a discount of 8% with a down payment of 50000 and 3 equal yearly installments and the rate of 20% pa. Find the value of the yearly installments.

a) 185674
b) 189651
c) 194637
d) 174342

Question 3: Raj borrowed an amount of Rs. 18900 at an interest rate of 10% pa, compounded annually. He repaid the entire amount in two equal installments – first installment at the end of the first year and the other at the end of the second year. Find the value of each installment.
a) Rs. 9450
b) Rs. 11430.5
c) Rs. 10890
d) Rs. 10017

Question 4: Slipkart, an online shopping portal, introduces two schemes for their customers, during a sale, on a washing machine whose price is Rs. 15000. In scheme 1 they sell the washing machine at 20% discount and in scheme 2 they sell it at a down payment of Rs. 5000 and three installments of Rs. 3000 payable at intervals of a year. Assuming that Slipkart invests its money at compound interest of 10% compounded anually, which offer is more profitable for them and by how much, at the end of three years?

a) Scheme 1, Rs. 613
b) Scheme 2, Rs. 613
c) Scheme 1, Rs. 1226
d) Scheme 2, Rs. 1226

Question 5: The compound interest offered on a sum of Rs 5000 is 8% calculated on a halfyearly basis for a period of 3 years. The borrower keeps paying back a sum of Rs 1000 at the end of every year. What is the amount that has to be paid at the end of the third year so as to clear all dues?

a) Rs 4705.1
b) Rs 4170.5
c) Rs 4075.1
d) Rs 4570.1

Solutions for CAT Questions on Installments:

Solutions:

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

Since there is a disount of 8% and a cash down payment of Rs 50000,
Effective price on which installments begin=92%ofRs5lakhs-Rs50000=Rs410000
Let the yearly installments be x
After one year,amount remaining after paying 1st installment= 1.2(410000)-x
After two years,amount remaining after paying 2nd installment=(1.2(1.2(410000)-x)-x)
Similarly after 3 years amount remaining=1.2(1.2(1.2(410000)-x)-x)-x=0
x=Rs 194637

Let the value of the installments Raj paid be x.
Total amount after 2 years = $18900 [1 + 0.1]^2$
He pays the first installment at the end of the first year and the second at the end of the second year.
Therefore,
$18900 [1 + 0.1]^2$ = $x [1 + 0.1] + x$
18900 * 1.21 = 2.1x
x = 10890

In Scheme 1 the washing machine will be sold at 20% discount, that is, for Rs. 12000.
The money earned by Slipkart at the end of three years is
$=12000\times(1.1)^{3}=15972$
In Scheme 2 Slipkart earns interest on 5000 for 3 years, 3000 for 2 years, 3000 for 1 year and no interest on the final 3000.
The money earned by Slipkart at the end of three years is
$=5000\times(1.1)^{3}+3000\times(1.1)^{2}+3000\times(1.1)+3000=16585$
So Slipkart earns Rs. 613 more in Scheme 2.

$5000*(1+4/100)^6$ = Rs 6326.6
Interest incurred on this payment at the end of the 3 years = $1000*(1+4/100)^4$ = Rs 1169.9
Interest incurred on this payment at the end of the 3 years = $1000*(1+4/100)^2$ = Rs 1081.6