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CAT 2018 Slot 1 — QA Question 3

InstallmentsEasy

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

Correct answer: 121000

Answer: 121000

Solution

Easy

The principal is Rs. 2,10,0002{,}10{,}000 at 10%10\% compounded annually, repaid in two equal instalments. Split the principal into the part XX repaid in year 1 and the rest in year 2. Write each instalment, set them equal, solve for XX, then compute the common instalment.

1

First instalment. One year's interest on the full principal plus the part XX of principal repaid.

interest year 1=210000×0.1=21000⇒ I1=21000+X\begin{aligned} &\text{interest year 1} = 210000\times0.1 = 21000\\ &\Rightarrow\ I_1 = 21000 + X \end{aligned}
2

Second instalment. The remaining principal (210000−X)(210000 - X) stays for one more year, growing by the 10%10\% factor 1.11.1.

I2=(210000−X)×1.1⇒ I2=231000−1.1X\begin{aligned} &I_2 = (210000 - X)\times 1.1\\ &\Rightarrow\ I_2 = 231000 - 1.1X \end{aligned}
3

Equal instalments. Set I1=I2I_1 = I_2 and solve for XX.

21000+X=231000−1.1X⇒ 2.1X=210000(collect X)⇒ X=100000\begin{aligned} &21000 + X = 231000 - 1.1X\\ &\Rightarrow\ 2.1X = 210000 \quad\text{(collect }X\text{)}\\ &\Rightarrow\ X = 100000 \end{aligned}
4

Value of each instalment. Substitute XX into I1I_1.

each instalment=21000+100000=121000\begin{aligned} &\text{each instalment} = 21000 + 100000 = 121000 \end{aligned}
Rs. 1,21,000\boxed{\text{Rs. } 1{,}21{,}000}

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CAT 2018 Slot 1 QA Q3: John borrowed Rs. 2,10,000 from a bank at an interest rate of 10% per annum, compounded annually. The loan was — Solution | TheCATExam