## A Factory Operator Bought a Diesel Generator

If a factory operator purchased a diesel generator, it means they acquired a generator that runs on diesel fuel. Diesel generators are commonly used in industrial settings to provide electricity during power outages or in areas where a stable power supply is not available. These generators are known for their reliability, durability, and ability to generate large amounts of power.

**By investing in a diesel generator, the factory operator can ensure the uninterrupted operation of critical machinery and equipment, safeguarding against potential losses caused by power disruptions.** The generator's capacity would depend on the specific power requirements of the factory, and it would be essential to properly maintain and service the generator to ensure optimal performance and longevity.

## Examples of A Factory Operator Bought a Diesel Generator

### Example 1:

A factory operator bought a diesel generator with a capacity of 500 kVA. The factory's average power consumption is 300 kW. Calculate the generator's utilization factor.

**Solution:** To find the utilization factor, we need to divide the factory's average power consumption by the generator's capacity and multiply by 100.

Utilization factor = (Average Power Consumption / Generator Capacity) * 100 Utilization factor = (300 kW / 500 kVA) * 100 Utilization factor = (0.6) * 100 Utilization factor = 60%

### Example 2:

A factory operator bought a diesel generator for $10,000. After 5 years, the operator decided to sell it at a depreciation rate of 10% per year. Calculate the selling price of the generator. (*Note: You can replace $ in Rupees)

**Solution:** To calculate the selling price, we need to apply the depreciation rate for 5 years and subtract the depreciation amount from the original cost.

Depreciation per year = Depreciation Rate * Original Cost Depreciation per year = 10% * $10,000 Depreciation per year = $1,000

Total Depreciation = Depreciation per year * Number of Years Total Depreciation = $1,000 * 5 Total Depreciation = $5,000

Selling Price = Original Cost - Total Depreciation Selling Price = $10,000 - $5,000 Selling Price = $5,000

Therefore, the selling price of the diesel generator is $5,000.

### Example 3:

A factory operator bought a diesel generator that consumes 8 liters of fuel per hour. If the cost of diesel is $1.50 per liter, calculate the cost of running the generator for 10 hours. (*Note: You can replace $ in Rupees)

**Solution:** To calculate the cost of running the generator, we need to multiply the fuel consumption rate (liters per hour) by the cost of diesel (dollars per liter) and then multiply by the number of hours.

Fuel Cost = Fuel Consumption Rate * Cost of Diesel * Number of Hours Fuel Cost = 8 liters/hour * $1.50/liter * 10 hours Fuel Cost = $120

Therefore, the cost of running the diesel generator for 10 hours is $120.

### Example 4:

A factory operator took a loan of $50,000 at an interest rate of 8% per annum for a period of 3 years. Calculate the total amount to be repaid at the end of the loan term. (*Note: You can replace $ in Rupees)

**Solution: **To calculate the total amount to be repaid, we need to consider both the principal amount (loan amount) and the interest accrued over the loan period.

Interest = Principal * Rate * Time Interest = $50,000 * 8% * 3 years Interest = $12,000

Total Amount to be Repaid = Principal + Interest Total Amount to be Repaid = $50,000 + $12,000 Total Amount to be Repaid = $62,000

Therefore, the factory operator has to repay a total amount of $62,000 at the end of the loan term.

### Example 5:

A factory operator invested $20,000 in a savings account that offers a compound interest rate of 6% per annum. If the interest is compounded annually, calculate the value of the investment after 5 years. (*Note: You can replace $ in Rupees)

**Solution: **To calculate the value of the investment, we can use the compound interest formula:

Amount = Principal * (1 + Rate)^Time

Amount = $20,000 * (1 + 6%/100)^5 Amount = $20,000 * (1 + 0.06)^5 Amount = $20,000 * (1.06)^5 Amount = $20,000 * 1.338225 Amount = $26,764.50

Therefore, the value of the investment after 5 years will be approximately $26,764.50.

### Example 6:

A factory operator borrowed $10,000 at an interest rate of 12% per annum compounded annually. If the loan is to be repaid in 3 equal annual installments, calculate the amount of each installment. (*Note: You can replace $ in Rupees)

**Solution:** To calculate the equal annual installments, we can use the formula for the present value of an annuity:

Installment Amount = Principal / ((1 - (1 + Rate)^(-Time)) / Rate)

Installment Amount = $10,000 / ((1 - (1 + 12%/100)^(-3)) / (12%/100)) Installment Amount = $10,000 / ((1 - (1 + 0.12)^(-3)) / 0.12) Installment Amount = $10,000 / ((1 - 1.404928) / 0.12) Installment Amount = $10,000 / (0.595072 / 0.12) Installment Amount = $10,000 / 4.958933 Installment Amount = $2,016.32 (approx.)

Therefore, the amount of each annual installment will be approximately $2,016.32.