In problems involving sinking funds, you can calculate the accumulated value using the formula \( A = P \cdot \frac{(1 + r)^n - 1}{r} \), where \( P \) is the principal, \( r \) is the interest rate per period, and \( n \) is the number of periods. The surplus is the amount accumulated over and above the initial total investment, which is crucial for assessing the effectiveness of the sinking fund. Be sure to carefully substitute and simplify the values to calculate the final surplus.
The sinking fund's accumulated value is determined by the formula:
\[ A = P \cdot \frac{(1 + r)^n - 1}{r}. \]
Given:
- \( P = 12,000 \),
- \( r = 0.05 \),
- \( n = 10 \),
- \( (1.05)^{10} \approx 1.6 \).
Substituting the values into the formula:
\[ A = 12,000 \cdot \frac{1.6 - 1}{0.05} = 12,000 \cdot \frac{0.6}{0.05} = 12,000 \cdot 12 = 1,44,000. \]
The resulting surplus is:
\[ \text{Surplus} = A - 72,000 = 1,44,000 - 72,000 = Rs.72,000. \]