If inflation increases at a rate of $8\%$ p.a., what will a ₹ $20$ article cost at the end of two years?

### Concept & Formula Inflation acts identically to compound interest. As the price increases in the first year, the second year's inflation is calculated on that new, higher price, not the original base price. The formula for the final amount after compound growth is: $$ A = P \left(1 + \frac{R}{100}\right)^T $$ ### Step-by-Step Solution 1. **Given Data:** * Initial Cost ($P$) = ₹ $20$ * Inflation Rate ($R$) = $8\%$ * Time ($T$) = $2$ years 2. **Apply the Formula:** * $$ \text{Final Cost} = 20 \times \left( 1 + \frac{8}{100} \right)^2 $$ * $$ = 20 \times (1.08)^2 $$ 3. **Calculate the Square:** * $1.08 \times 1.08 = 1.1664$ 4. **Find the Final Value:** * $$ \text{Final Cost} = 20 \times 1.1664 $$ * $$ = 23.328 $$ 5. **Evaluate Options:** * The value ₹ $23.328$ falls strictly between ₹ $23$ and ₹ $24$. ### Exam Strategy & Shortcut Use the successive percentage formula: $X + Y + \frac{X \times Y}{100}$. For two years at $8\%$, the net effective increase is: $$ 8 + 8 + \frac{8 \times 8}{100} = 16 + 0.64 = 16.64\% $$ Now, simply find $16.64\%$ of ₹ $20$: $$ 20 \times 0.1664 = 3.328 $$ Add this increase to the original ₹ $20$ to get ₹ $23.328$. This clearly places the answer in the ₹ $23$ to ₹ $24$ range. ### Common Pitfall A common error is treating inflation as simple interest, calculating $8\% + 8\% = 16\%$, and finding $116\%$ of $20$, which equals $23.2$. While $23.2$ still happens to fall in the correct bracket for this specific question, relying on simple interest will lead to incorrect answers when options are tighter. ### Final Answer **Therefore, the correct answer is Between ₹ $23$ and ₹ $24$.**