MACHINE COST = 520000
AFTER 25 YEARS = 520000 + 25% = 650000
SCRAP VALUE = 25000
MONEY REQUIRED = 650000 - 25000
= 625000
FUTURE VALUE = 625000
FUTURE VALUE FORMULA = ANUITY× ( 1.035) RAISE TO 25 -1
÷
0.035
625000 = ANNUITY( 1.035) RAISE TO 25 - 1
÷
0.035
ANNUITY = 625000
÷
38.949

ANNUITY = 16046.27..take nearest value 16050

Calculation for Sinking Fund:

To determine the amount that should be set aside every year for the sinking fund, we need to consider the cost of the new machine after 25 years, the scrap value realization, and the interest rate at which the sinking fund investments accumulate.

1. Cost of the new machine after 25 years:
The cost of the new machine will be 25% higher than the original cost of ₹520000. Therefore, the cost of the new machine after 25 years will be:

Cost of new machine = ₹520000 + 25% of ₹520000
= ₹520000 + (25/100) * ₹520000
= ₹520000 + ₹130000
= ₹650000

2. Scrap value realization:
The scrap value realization is the amount that can be obtained by selling the old machine after 25 years. In this case, the scrap value realization is ₹25000.

3. Sinking fund investments accumulate at 3.5% compound interest p.a.:
The sinking fund investments accumulate at a compound interest rate of 3.5% per annum. This means that the amount set aside every year will accumulate and earn interest at a rate of 3.5% per annum.

Calculation of annual sinking fund amount:
The sinking fund amount can be calculated using the sinking fund formula:

Sinking fund amount = (Cost of new machine - Scrap value realization) / (1 + interest rate)^n - 1 / interest rate

Where:
- Cost of new machine = ₹650000
- Scrap value realization = ₹25000
- Interest rate = 3.5% = 0.035
- n = 25 years

Sinking fund amount = (₹650000 - ₹25000) / (1 + 0.035)^25 - 1 / 0.035

Using this formula, the sinking fund amount can be calculated.

Explanation of the Time Value of Money:

The concept of time value of money is based on the principle that the value of money changes over time due to factors such as inflation, interest rates, and the opportunity cost of investing money elsewhere. In this case, the sinking fund is created to account for the future cost of replacing the machine.

By setting aside a certain amount of money every year and investing it in a sinking fund, the accumulated funds will grow over time due to compound interest. This ensures that sufficient funds are available to replace the machine at the end of its estimated life.

The sinking fund amount is calculated based on the future cost of the new machine, taking into account the scrap value realization and the interest rate at which the funds accumulate. By considering these factors, the sinking fund amount can be determined to ensure that enough funds are available to replace the machine at the end of its estimated life.

The sinking fund concept helps to manage the financial aspect of replacing assets or equipment in the future. It allows for systematic savings and investment to ensure that the required funds are available when needed. By considering the time value of money, the sinking fund takes into account the changes in the value of money over time and ensures that sufficient funds are set aside to meet future expenses.