A municipal corporation needs to accumulate Rs. 10 crores after 20 years for the replacement of a major bridge. They decide to deposit an equal amount at the end of each year into a sinking fund that earns 8% annual compound interest. The sinking fund factor (A/F, i, n) for i = 8% and n = 20 years is 0.02185. What is the annual deposit required (in Rs. crores)?
- A0.2185Correct
- B2.185
- C21.85
- D0.02185
Solution
Concept
Sinking fund calculation using sinking fund factor
Formula
A = F × (A/F, i, n)
Step-by-step solution
1. Given data: - Future accumulated replacement cost (F) = Rs. 10 crores - Sinking Fund Factor (A/F, 8%, 20 yrs) = 0.02185 2. Formula for uniform annual sinking fund payment: A = F × (A/F, i, n) 3. Compute deposit: A = 10 × 0.02185 = 0.2185 crores. 4. Therefore, option A (0.2185) is the correct amount. Answer: A
Explanation
In valuation and engineering economics, the annual sinking fund deposit (A) required to accumulate a future target sum (F) is given by: A = F × Sinking Fund Factor (A/F, i, n). For F = Rs. 10 crores and SFF = 0.02185, Annual Deposit = 10 × 0.02185 = Rs. 0.2185 crores.
Why the other options are wrong
B) 2.185 crores represents 100 × SFF, an order of magnitude too high. C) 21.85 crores exceeds the total future accumulated replacement sum itself. D) 0.02185 crores is the value of SFF, omitting multiplication by the 10 crores fund target.
Shortcut
Annual Deposit = Target Amount × SFF = 10 × 0.02185 = 0.2185 crores.
Common mistake
Misplacing the decimal point by dividing or multiplying by 100.
Correct answer: A) 0.2185