Discussion
Amit gave his friend Rs. 11000. This was to be repaid in 2 yearly installments with a rate of interest of 20% compounded annually. How much would be the value of each installment?
Answer: A
Discount both installments back to the present at 20%.
\[ \frac{x}{1.2} + \frac{x}{(1.2)^{2}} = 11000 \]
\[ x\left(\frac{5}{6} + \frac{25}{36}\right) = x \times \frac{55}{36} = 11000 \]
\[ x = \frac{11000 \times 36}{55} = \text{Rs. } 7200 \]
Checking: after one year the debt is \( 11000 \times 1.2 = 13200 \); paying 7200 leaves 6000, which grows to 7200 by the second year and is cleared exactly.
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