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How much money must set a side each year so as to replace a machine that will cost Rs 15,000 After 8 years ? the rate of interest being 12% per year compound solve this
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Calculation of the Annual Deposit Required to Replace a Machine
To calculate the amount of money that needs to be set aside each year to replace a machine costing Rs 15,000 after 8 years, we can use the compound interest formula. The formula for compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (Rs 15,000)
P = the principal amount (initial cost of the machine)
r = annual interest rate (12%)
n = number of times interest is compounded per year (assuming it is compounded annually)
t = number of years (8)
By rearranging the formula, we can solve for the principal amount P, which represents the annual deposit required to replace the machine:
P = A / (1 + r/n)^(nt)
Now, let's calculate the annual deposit required step by step:
1. Determine the values:
A = Rs 15,000
r = 12% (or 0.12)
n = 1 (compounded annually)
t = 8 years
2. Substitute the values into the formula:
P = Rs 15,000 / (1 + 0.12/1)^(1*8)
3. Simplify the exponent:
P = Rs 15,000 / (1 + 0.12)^(8)
4. Calculate the denominator:
(1 + 0.12)^8 = 1.12^8 ≈ 2.1486
5. Divide the numerator by the denominator:
P ≈ Rs 15,000 / 2.1486
6. Calculate the annual deposit:
P ≈ Rs 6,982.42
Therefore, an annual deposit of approximately Rs 6,982.42 should be set aside each year to replace the machine costing Rs 15,000 after 8 years, assuming a compound interest rate of 12% per year.
To calculate the amount of money that needs to be set aside each year to replace a machine costing Rs 15,000 after 8 years, we can use the compound interest formula. The formula for compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (Rs 15,000)
P = the principal amount (initial cost of the machine)
r = annual interest rate (12%)
n = number of times interest is compounded per year (assuming it is compounded annually)
t = number of years (8)
By rearranging the formula, we can solve for the principal amount P, which represents the annual deposit required to replace the machine:
P = A / (1 + r/n)^(nt)
Now, let's calculate the annual deposit required step by step:
1. Determine the values:
A = Rs 15,000
r = 12% (or 0.12)
n = 1 (compounded annually)
t = 8 years
2. Substitute the values into the formula:
P = Rs 15,000 / (1 + 0.12/1)^(1*8)
3. Simplify the exponent:
P = Rs 15,000 / (1 + 0.12)^(8)
4. Calculate the denominator:
(1 + 0.12)^8 = 1.12^8 ≈ 2.1486
5. Divide the numerator by the denominator:
P ≈ Rs 15,000 / 2.1486
6. Calculate the annual deposit:
P ≈ Rs 6,982.42
Therefore, an annual deposit of approximately Rs 6,982.42 should be set aside each year to replace the machine costing Rs 15,000 after 8 years, assuming a compound interest rate of 12% per year.
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How much money must set a side each year so as to replace a machine that will cost Rs 15,000 After 8 years ? the rate of interest being 12% per year compound solve this? for B Com 2024 is part of B Com preparation. The Question and answers have been prepared according to the B Com exam syllabus. Information about How much money must set a side each year so as to replace a machine that will cost Rs 15,000 After 8 years ? the rate of interest being 12% per year compound solve this? covers all topics & solutions for B Com 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How much money must set a side each year so as to replace a machine that will cost Rs 15,000 After 8 years ? the rate of interest being 12% per year compound solve this?.
How much money must set a side each year so as to replace a machine that will cost Rs 15,000 After 8 years ? the rate of interest being 12% per year compound solve this? for B Com 2024 is part of B Com preparation. The Question and answers have been prepared according to the B Com exam syllabus. Information about How much money must set a side each year so as to replace a machine that will cost Rs 15,000 After 8 years ? the rate of interest being 12% per year compound solve this? covers all topics & solutions for B Com 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How much money must set a side each year so as to replace a machine that will cost Rs 15,000 After 8 years ? the rate of interest being 12% per year compound solve this?.
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