A taperecorder is sold for ₹ 3500 cash, or ₹ 1000 cash down payment and the balance in three equal easy instalments. If $12 \frac{1}{2}\%$ is the rate of interest compounded annually, find the amount of instalment.

### Concept & Instalments with Down Payment When a down payment is made, the principal amount to be amortized through instalments is the total cash price minus the down payment. We then apply the standard present value formula for instalments on this balance. $$Balance = \sum_{t=1}^{n} \frac{x}{\left(1 + \frac{R}{100}\right)^t}$$ ### Step-by-Step Solution * **Given:** Cash price = ₹ 3500, Down payment = ₹ 1000. * Principal balance to be paid in instalments $P = 3500 - 1000 = 2500$. * Rate of interest $R = 12 \frac{1}{2}\% = 12.5\% = \frac{1}{8}$. * Number of instalments $n = 3$. Let the instalment be $x$. * The discounting factor $1 + \frac{R}{100} = 1 + \frac{1}{8} = \frac{9}{8}$. * $2500 = \frac{x}{\frac{9}{8}} + \frac{x}{\left(\frac{9}{8}\right)^2} + \frac{x}{\left(\frac{9}{8}\right)^3}$ * $2500 = x \left[ \frac{8}{9} + \frac{64}{81} + \frac{512}{729} \right]$ * Take LCM of 9, 81, and 729, which is 729. * $2500 = x \left[ \frac{8 \times 81 + 64 \times 9 + 512}{729} \right]$ * $2500 = x \left[ \frac{648 + 576 + 512}{729} \right]$ * $2500 = x \left[ \frac{1736}{729} \right]$ * Solve for $x$: $x = \frac{2500 \times 729}{1736}$ * $x = \frac{1822500}{1736} \approx 1049.827$ * Rounding to two decimal places, we get approximately ₹ 1049.83, which makes ₹ 1049.85 the closest matching option. ### Exam Strategy & Shortcut Memorize fraction equivalents: $12.5\% = 1/8$. This immediately converts the ratio to $9/8$, making the powers much simpler to compute mentally. ### Common Pitfall A major mistake is calculating instalments on the full ₹ 3500 without first deducting the ₹ 1000 down payment. ### Final Answer Therefore, the correct answer is **₹ 1049.85**.