Equal Instalments Loan Repayment

CAT 2019 Slot 1 · QA · Medium · SI & CI

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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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