CAT 2018 Slot 1 — QA Question 3
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., is
Answer & solution
Answer: 121000
Let the part of principal amount in the first instalment be Rs. X.
Interest for the first year on Rs. 2,10,0000 = 210000 × 0.1 = 21,000
∴ The first instalment = (21000 + X)
Remaining part of the principal = (210000 – X)
Amount due on this principal of (210000 – X) = (210000 – X) × 1.1 = 231000 – 1.1X
∴ The second instalment = 231000 – 1.1X
∴ 21000 + X = 231000 – 1.1X
Solving this, we get X = 1,00,000
∴ Each instalment = 100000 + 21000 = Rs. 1,21,000
Hence, 121000.