CAT Quantitative Aptitude Questions | CAT Simple and compound interest - Installments

The question is from CAT Simple and compound interest. 2IIMs CAT question bank provides you with CAT questions that can help you gear for CAT Exam CAT 2023. Simple Interest and Compound Interest is an important topic for CAT Preparation. This question is about a person paying the amount in three annual installments which is borrowed at 10% compound interest.

Question 15: Krishna borrows Rs. 45K from a bank at 10% compound interet. He repays it in three annual installments that are in arithmetic progression. He ends up paying 54K totally. How much did he pay in year 1?

1. Rs. 16,500
2. Rs. 19,500
3. Rs. 21,000
4. Rs. 18,000

Video Explanation

Explanatory Answer

Method of solving this CAT Question from Simple and compound interest: Find the common difference of AP and you are through.

Let the repayments be Rs "a – d", Rs "a" and Rs. "a + d"
a – d + a + a + d = 54000
3a = 54000
a = 18000
The payment at the end of year 2 is Rs. 18,000.
Borrowed amount = Rs. 45,000
Amount outstanding at the end of Year 1 = (45000 × 1.1) – (18000 – d)
= 31500 + d
Amount outstanding at the end of Year 2 = ((31500 + d) * 1.1) – 18000
= 34650 + 1.1d – 18000 = 16650 + 1.1d
Amount outstanding at the end of Year 3 = ((16650 + 1.1d) * 1.1) = 18000 + d
18315 + 1.21d = 18000 + d
0.21d = – 315
d = –1500
The payments are Rs. 19500, Rs. 18000 and Rs. 16500

The question is " How much did he pay in year 1?"
He paid Rs. 19500 in year 1

Hence, the answer is Rs. 19500.

Choice B is the correct answer.