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What sum should be invested at the end of each year so as to accumulate an amount of 796870 at the end of 10 years at the rate of 10% compounded annually
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What sum should be invested at the end of each year so as to accumulat...
Calculation of Annual Investment Required
Investment required at the end of each year to accumulate a desired amount at a specific interest rate can be calculated using the formula for future value of an annuity:
FV = Pmt * [(1 + r)^n - 1] / r
Where:
- FV = Future Value (796870 in this case)
- Pmt = Annual Investment
- r = Interest Rate (10% or 0.10)
- n = Number of Years (10 years)
Calculation Steps
1. Plug in the values into the formula:
796870 = Pmt * [(1 + 0.10)^10 - 1] / 0.10
2. Simplify the equation:
796870 = Pmt * [(1.10)^10 - 1] / 0.10
796870 = Pmt * [2.5937 - 1] / 0.10
796870 = Pmt * 1.5937 / 0.10
796870 = Pmt * 15.937
3. Solve for Pmt:
Pmt = 796870 / 15.937
Pmt ≈ 49931.37
Annual Investment Required
Therefore, an annual investment of approximately $49931.37 should be made at the end of each year for 10 years at a 10% interest rate in order to accumulate a total amount of $796870.
Investment required at the end of each year to accumulate a desired amount at a specific interest rate can be calculated using the formula for future value of an annuity:
FV = Pmt * [(1 + r)^n - 1] / r
Where:
- FV = Future Value (796870 in this case)
- Pmt = Annual Investment
- r = Interest Rate (10% or 0.10)
- n = Number of Years (10 years)
Calculation Steps
1. Plug in the values into the formula:
796870 = Pmt * [(1 + 0.10)^10 - 1] / 0.10
2. Simplify the equation:
796870 = Pmt * [(1.10)^10 - 1] / 0.10
796870 = Pmt * [2.5937 - 1] / 0.10
796870 = Pmt * 1.5937 / 0.10
796870 = Pmt * 15.937
3. Solve for Pmt:
Pmt = 796870 / 15.937
Pmt ≈ 49931.37
Annual Investment Required
Therefore, an annual investment of approximately $49931.37 should be made at the end of each year for 10 years at a 10% interest rate in order to accumulate a total amount of $796870.
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What sum should be invested at the end of each year so as to accumulate an amount of 796870 at the end of 10 years at the rate of 10% compounded annually?
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What sum should be invested at the end of each year so as to accumulate an amount of 796870 at the end of 10 years at the rate of 10% compounded annually? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about What sum should be invested at the end of each year so as to accumulate an amount of 796870 at the end of 10 years at the rate of 10% compounded annually? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What sum should be invested at the end of each year so as to accumulate an amount of 796870 at the end of 10 years at the rate of 10% compounded annually?.
What sum should be invested at the end of each year so as to accumulate an amount of 796870 at the end of 10 years at the rate of 10% compounded annually? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about What sum should be invested at the end of each year so as to accumulate an amount of 796870 at the end of 10 years at the rate of 10% compounded annually? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What sum should be invested at the end of each year so as to accumulate an amount of 796870 at the end of 10 years at the rate of 10% compounded annually?.
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