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Sagot :
Certainly! Let's go through each part of the request step-by-step and show all the formulas and workings.
### (a) Calculate profits for the year 2021 and 2023
To calculate profit, we use the formula:
[tex]\[ \text{Profit} = \left(\frac{\text{Returns on Capital (\%)}}{100}\right) \times \text{Capital} \][/tex]
For 2021:
[tex]\[ \text{Returns on Capital (2021)} = 35\% \][/tex]
[tex]\[ \text{Capital (2021)} = 650,000 \][/tex]
[tex]\[ \text{Profit (2021)} = \left(\frac{35}{100}\right) \times 650,000 \][/tex]
[tex]\[ \text{Profit (2021)} = 0.35 \times 650,000 \][/tex]
[tex]\[ \text{Profit (2021)} = 227,500 \][/tex]
For 2023:
[tex]\[ \text{Returns on Capital (2023)} = 45\% \][/tex]
[tex]\[ \text{Capital (2023)} = 975,000 \][/tex]
[tex]\[ \text{Profit (2023)} = \left(\frac{45}{100}\right) \times 975,000 \][/tex]
[tex]\[ \text{Profit (2023)} = 0.45 \times 975,000 \][/tex]
[tex]\[ \text{Profit (2023)} = 438,750 \][/tex]
### (b) Calculate returns on capital for the year 2022
To calculate returns on capital, we use the formula:
[tex]\[ \text{Returns on Capital (\%)} = \left(\frac{\text{Profit}}{\text{Capital}}\right) \times 100 \][/tex]
For 2022:
[tex]\[ \text{Profit (2022)} = 117,000 \][/tex]
[tex]\[ \text{Capital (2022)} = 585,000 \][/tex]
[tex]\[ \text{Returns on Capital (2022)} = \left(\frac{117,000}{585,000}\right) \times 100 \][/tex]
[tex]\[ \text{Returns on Capital (2022)} = 0.2 \times 100 \][/tex]
[tex]\[ \text{Returns on Capital (2022)} = 20\% \][/tex]
### (c) Calculate the percentage increase in profit between year 2022 and 2023
To calculate the percentage increase, we use the formula:
[tex]\[ \text{Percentage Increase} = \left( \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \right) \times 100 \][/tex]
Between 2022 and 2023:
[tex]\[ \text{Profit (2022)} = 117,000 \][/tex]
[tex]\[ \text{Profit (2023)} = 438,750 \][/tex]
[tex]\[ \text{Percentage Increase} = \left( \frac{438,750 - 117,000}{117,000} \right) \times 100 \][/tex]
[tex]\[ \text{Percentage Increase} = \left( \frac{321,750}{117,000} \right) \times 100 \][/tex]
[tex]\[ \text{Percentage Increase} = 2.75 \times 100 \][/tex]
[tex]\[ \text{Percentage Increase} = 275\% \][/tex]
### (d) Calculate the percentage decrease in profit between year 2021 and 2022
To calculate the percentage decrease, we use the formula:
[tex]\[ \text{Percentage Decrease} = \left( \frac{\text{Old Value} - \text{New Value}}{\text{Old Value}} \right) \times 100 \][/tex]
Between 2021 and 2022:
[tex]\[ \text{Profit (2021)} = 227,500 \][/tex]
[tex]\[ \text{Profit (2022)} = 117,000 \][/tex]
[tex]\[ \text{Percentage Decrease} = \left( \frac{227,500 - 117,000}{227,500} \right) \times 100 \][/tex]
[tex]\[ \text{Percentage Decrease} = \left( \frac{110,500}{227,500} \right) \times 100 \][/tex]
[tex]\[ \text{Percentage Decrease} = 0.485 \times 100 \][/tex]
[tex]\[ \text{Percentage Decrease} = 48.5\% \][/tex]
### (e) Calculate the increase in capital between year 2022 and 2023
To calculate the increase in capital, we use the formula:
[tex]\[ \text{Increase in Capital} = \text{Capital (New Year)} - \text{Capital (Old Year)} \][/tex]
Between 2022 and 2023:
[tex]\[ \text{Capital (2023)} = 975,000 \][/tex]
[tex]\[ \text{Capital (2022)} = 585,000 \][/tex]
[tex]\[ \text{Increase in Capital} = 975,000 - 585,000 \][/tex]
[tex]\[ \text{Increase in Capital} = 390,000 \][/tex]
### (f) Calculate the decrease in capital between year 2021 and 2022
To calculate the decrease in capital, we use a similar formula:
[tex]\[ \text{Decrease in Capital} = \text{Capital (Old Year)} - \text{Capital (New Year)} \][/tex]
Between 2021 and 2022:
[tex]\[ \text{Capital (2021)} = 650,000 \][/tex]
[tex]\[ \text{Capital (2022)} = 585,000 \][/tex]
[tex]\[ \text{Decrease in Capital} = 650,000 - 585,000 \][/tex]
[tex]\[ \text{Decrease in Capital} = 65,000 \][/tex]
Summarizing all results:
1. Profit (2021): N227,500
2. Profit (2023): N438,750
3. Returns on Capital (2022): 20%
4. Percentage Increase in Profit (2022 to 2023): 275%
5. Percentage Decrease in Profit (2021 to 2022): 48.5%
6. Increase in Capital (2022 to 2023): N390,000
7. Decrease in Capital (2021 to 2022): N65,000
### (a) Calculate profits for the year 2021 and 2023
To calculate profit, we use the formula:
[tex]\[ \text{Profit} = \left(\frac{\text{Returns on Capital (\%)}}{100}\right) \times \text{Capital} \][/tex]
For 2021:
[tex]\[ \text{Returns on Capital (2021)} = 35\% \][/tex]
[tex]\[ \text{Capital (2021)} = 650,000 \][/tex]
[tex]\[ \text{Profit (2021)} = \left(\frac{35}{100}\right) \times 650,000 \][/tex]
[tex]\[ \text{Profit (2021)} = 0.35 \times 650,000 \][/tex]
[tex]\[ \text{Profit (2021)} = 227,500 \][/tex]
For 2023:
[tex]\[ \text{Returns on Capital (2023)} = 45\% \][/tex]
[tex]\[ \text{Capital (2023)} = 975,000 \][/tex]
[tex]\[ \text{Profit (2023)} = \left(\frac{45}{100}\right) \times 975,000 \][/tex]
[tex]\[ \text{Profit (2023)} = 0.45 \times 975,000 \][/tex]
[tex]\[ \text{Profit (2023)} = 438,750 \][/tex]
### (b) Calculate returns on capital for the year 2022
To calculate returns on capital, we use the formula:
[tex]\[ \text{Returns on Capital (\%)} = \left(\frac{\text{Profit}}{\text{Capital}}\right) \times 100 \][/tex]
For 2022:
[tex]\[ \text{Profit (2022)} = 117,000 \][/tex]
[tex]\[ \text{Capital (2022)} = 585,000 \][/tex]
[tex]\[ \text{Returns on Capital (2022)} = \left(\frac{117,000}{585,000}\right) \times 100 \][/tex]
[tex]\[ \text{Returns on Capital (2022)} = 0.2 \times 100 \][/tex]
[tex]\[ \text{Returns on Capital (2022)} = 20\% \][/tex]
### (c) Calculate the percentage increase in profit between year 2022 and 2023
To calculate the percentage increase, we use the formula:
[tex]\[ \text{Percentage Increase} = \left( \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \right) \times 100 \][/tex]
Between 2022 and 2023:
[tex]\[ \text{Profit (2022)} = 117,000 \][/tex]
[tex]\[ \text{Profit (2023)} = 438,750 \][/tex]
[tex]\[ \text{Percentage Increase} = \left( \frac{438,750 - 117,000}{117,000} \right) \times 100 \][/tex]
[tex]\[ \text{Percentage Increase} = \left( \frac{321,750}{117,000} \right) \times 100 \][/tex]
[tex]\[ \text{Percentage Increase} = 2.75 \times 100 \][/tex]
[tex]\[ \text{Percentage Increase} = 275\% \][/tex]
### (d) Calculate the percentage decrease in profit between year 2021 and 2022
To calculate the percentage decrease, we use the formula:
[tex]\[ \text{Percentage Decrease} = \left( \frac{\text{Old Value} - \text{New Value}}{\text{Old Value}} \right) \times 100 \][/tex]
Between 2021 and 2022:
[tex]\[ \text{Profit (2021)} = 227,500 \][/tex]
[tex]\[ \text{Profit (2022)} = 117,000 \][/tex]
[tex]\[ \text{Percentage Decrease} = \left( \frac{227,500 - 117,000}{227,500} \right) \times 100 \][/tex]
[tex]\[ \text{Percentage Decrease} = \left( \frac{110,500}{227,500} \right) \times 100 \][/tex]
[tex]\[ \text{Percentage Decrease} = 0.485 \times 100 \][/tex]
[tex]\[ \text{Percentage Decrease} = 48.5\% \][/tex]
### (e) Calculate the increase in capital between year 2022 and 2023
To calculate the increase in capital, we use the formula:
[tex]\[ \text{Increase in Capital} = \text{Capital (New Year)} - \text{Capital (Old Year)} \][/tex]
Between 2022 and 2023:
[tex]\[ \text{Capital (2023)} = 975,000 \][/tex]
[tex]\[ \text{Capital (2022)} = 585,000 \][/tex]
[tex]\[ \text{Increase in Capital} = 975,000 - 585,000 \][/tex]
[tex]\[ \text{Increase in Capital} = 390,000 \][/tex]
### (f) Calculate the decrease in capital between year 2021 and 2022
To calculate the decrease in capital, we use a similar formula:
[tex]\[ \text{Decrease in Capital} = \text{Capital (Old Year)} - \text{Capital (New Year)} \][/tex]
Between 2021 and 2022:
[tex]\[ \text{Capital (2021)} = 650,000 \][/tex]
[tex]\[ \text{Capital (2022)} = 585,000 \][/tex]
[tex]\[ \text{Decrease in Capital} = 650,000 - 585,000 \][/tex]
[tex]\[ \text{Decrease in Capital} = 65,000 \][/tex]
Summarizing all results:
1. Profit (2021): N227,500
2. Profit (2023): N438,750
3. Returns on Capital (2022): 20%
4. Percentage Increase in Profit (2022 to 2023): 275%
5. Percentage Decrease in Profit (2021 to 2022): 48.5%
6. Increase in Capital (2022 to 2023): N390,000
7. Decrease in Capital (2021 to 2022): N65,000
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