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 2019. 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?

- Rs. 16,500
- Rs. 19,500
- Rs. 21,000
- Rs. 18,000

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

Choice B is the correct answer.

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