Calculating the Annual Sinking Fund Amount

To calculate the annual sinking fund amount, we need to consider the following factors:

1. Initial cost of the machine: The machine costs 520,000₹.
2. Estimated life of the machine: The machine has an estimated life of 25 years.
3. Replacement cost: The replacement cost is 25% higher than the initial cost, i.e., 520,000₹ * 1.25 = 650,000₹.
4. Scrap value: After 25 years, the machine will have a scrap value of 25,000₹.
5. Compound interest rate: The sinking fund investment will accumulate compound interest at a rate of 3.5% per year.

Step 1: Calculate the Depreciation Amount

The depreciation amount per year can be calculated using the formula:

Depreciation amount = (Initial cost - Scrap value) / Estimated life

Depreciation amount = (520,000₹ - 25,000₹) / 25 = 19,800₹

Step 2: Calculate the Annual Sinking Fund Amount

The sinking fund amount per year can be calculated using the formula:

Sinking fund amount = (Replacement cost - Scrap value) / Present value factor

Present value factor = (1 - (1 + Compound interest rate)^(-Estimated life)) / Compound interest rate

Present value factor = (1 - (1 + 0.035)^(-25)) / 0.035 = 15.257

Sinking fund amount = (650,000₹ - 25,000₹) / 15.257 = 41,512.08₹

Therefore, the amount that should be set aside every year in the sinking fund is approximately 41,512.08₹.

Explanation:

The sinking fund is created to accumulate enough funds over a certain period of time to replace the machine when it reaches the end of its useful life. In this case, the machine has an estimated life of 25 years.

To calculate the annual sinking fund amount, we first need to determine the depreciation amount per year. The depreciation amount is the difference between the initial cost of the machine and its scrap value, divided by the estimated life of the machine. In this case, the depreciation amount is 19,800₹ per year.

Next, we calculate the present value factor, which takes into account the compound interest rate and the estimated life of the machine. The present value factor is used to calculate the sinking fund amount per year. In this case, the present value factor is 15.257.

Finally, we calculate the sinking fund amount per year by subtracting the scrap value from the replacement cost and dividing it by the present value factor. The sinking fund amount is approximately 41,512.08₹ per year.

By setting aside this amount every year in the sinking fund and investing it at a compound interest rate of 3.5%, we will accumulate enough funds to replace the machine after 25 years.