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Equal Instalments Loan Repayment

CAT 2019 Slot 1 · Quantitative Ability · Medium · SI & CI

This is a medium Quantitative Ability question from the CAT 2019 Slot 1 paper. It tests SI & CI. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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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

121000

Explanation

Let each instalment be XX. Present value of XX due in 1 year + Present value of XX due in 2 years = 2,10,0002,10,000. X1.1+X1.21=2,10,000\frac{X}{1.1} + \frac{X}{1.21} = 2,10,000 X(1.1+11.21)=2,10,000⇒X⋅2.11.21=2,10,000X \left(\frac{1.1 + 1}{1.21}\right) = 2,10,000 \Rightarrow X \cdot \frac{2.1}{1.21} = 2,10,000 X=1,00,000×1.21=1,21,000X = 1,00,000 \times 1.21 = 1,21,000.

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