Discussion
Amit gave his friend Rs. 11000. This loan was to be repaid in 3 yearly installments with a rate of interest of 20% compounded annually. How much would be the value of each installment?
Answer: B
Each installment is discounted back to today at 20%, and the three present values must add to the loan.
\[ \frac{x}{1.2} + \frac{x}{(1.2)^{2}} + \frac{x}{(1.2)^{3}} = 11000 \]
\[ x\left(0.833333 + 0.694444 + 0.578704\right) = 11000 \]
\[ 2.106481\,x = 11000 \quad\Longrightarrow\quad x = \text{Rs. } 5221.97 \]
Simply dividing Rs. 11,000 by three gives Rs. 3666.67 - the first option - but that ignores the interest accruing between installments.
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