CA Foundation · Quantitative Aptitude · Mathematics of Finance
Sundaram Textiles needs Rs 5,00,000 at the end of 3 years to replace a machine. It deposits an equal amount at the end of each year in a sinking fund earning 10% p.a. compound interest. The approximate annual deposit is:
The annual deposit is about Rs 1,51,057. Using the sinking fund formula, multiply Rs 5,00,000 by 10% and divide by the compounding factor 1.331 minus 1, which is 0.331. Interest earned reduces the deposit below the simple split of Rs 1,66,667.
- ARs 1,37,326
- BRs 1,51,057Correct
- CRs 1,66,667
- DRs 1,50,000
Explanation
Deposit = FV × i / ((1+i)^n − 1) = 5,00,000 × 0.10 / (1.331 − 1) = 50,000 / 0.331 ≈ Rs 1,51,057. Rs 1,66,667 ignores interest (5,00,000 / 3), and Rs 1,37,326 wrongly treats deposits as made at the start of each year.
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