The present worth of ₹ 169 due in 2 years at 4% per annum compound interest is

### Concept & Logic "Present worth" is simply the Principal ($P$) that needs to be invested today to yield a specific future Amount ($A$) under compound interest. $$P = \frac{A}{\left(1 + \frac{R}{100}\right)^n}$$ ### Step-by-Step Solution * Given Future Amount $A = 169$ * Time $n = 2$ years * Rate $R = 4\%$ p.a. * Convert $4\%$ to a fraction: $4\% = \frac{4}{100} = \frac{1}{25}$. * The multiplier is $\left(1 + \frac{1}{25}\right) = \frac{26}{25}$. * Substitute into the formula: $P = \frac{169}{\left(\frac{26}{25}\right)^2}$ $P = 169 \times \left(\frac{25}{26}\right)^2$ $P = 169 \times \frac{625}{676}$ * Simplify the expression. Notice that $169$ and $676$ are related. $169 \times 4 = 676$. (Alternatively, $13^2 = 169$ and $26^2 = 676$). So, $P = \frac{169 \times 625}{169 \times 4}$ $P = \frac{625}{4}$ * Evaluate the final fraction: $P = 156.25$ ### Exam Strategy & Shortcut Instead of dealing with large multiplications, break numbers into prime factors or recognizable squares early. Seeing $169$ as $13^2$ and $26$ as $13 \times 2$ makes the cancellation obvious without doing heavy division. ### Common Pitfall Confusing "Present Worth" in a compound interest context with formulas for "True Discount", which are primarily used in simple interest or specific commercial discounting scenarios. ### Final Answer Therefore, the correct answer is **₹ 156.25**.