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Question 15: 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:[TITA]


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Explanatory Answer

Method of solving this CAT Question from SI and CI
Installments

Given, money borrowed = Rs. 2,10,000
At 10% Interest, after 1 year
Outstanding amount = Rs. 1.1 × 2,10,000 = Rs. 2,31,000
Let the First Installment be x
So, Due amount = Rs. 2,31,000 - x

This due amount is carried over to the second year, with an interest of 10%
So, Outstanding amount for Second year = Rs. 1.1 × (2,31,000 - x)
This amount will be payed as Second Installment
We know, Installment for year 1 = Installment for year 2 = Rs. x
1.1 × (2,31,000 - x) = x
2.1 x = 2,54,100
x = Rs. 1,21,000

The question is "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"

Hence, the answer is Rs. 1,21,000.

 

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