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A invests 22000 in a bank at 4% interest compounded semi-annually for11. 6 years. B invests some money in the same scheme for 5 years, theninvests in another bank at 10% simple interest for 1 year. If the amountreceived by both at the end of 6 years was equal, how much money didB invest?
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A invests 22000 in a bank at 4% interest compounded semi-annually for1...
Given:
A invests $22,000 in a bank at 4% interest compounded semi-annually for 11.6 years.
To find:
The amount of money B invested.
Calculating the amount received by A:
We can use the compound interest formula to calculate the amount received by A at the end of 6 years.
The formula for compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
Plugging in the values:
P = $22,000
r = 4% = 0.04
n = 2 (semi-annually compounded)
t = 11.6 years
A = 22000(1 + 0.04/2)^(2 * 11.6)
A = 22000(1 + 0.02)^(23.2)
A = 22000(1.02)^(23.2)
A = 22000 * 1.5735
A = $34,617
Calculating the amount received by B:
Let's assume B invested an amount x in the same scheme for 5 years.
Using the same compound interest formula, we can calculate the amount received by B at the end of 5 years.
P = x
r = 4% = 0.04
n = 2 (semi-annually compounded)
t = 5 years
B = x(1 + 0.04/2)^(2 * 5)
B = x(1 + 0.02)^(10)
B = x(1.02)^(10)
After 5 years, B withdraws the amount and invests it in another bank at 10% simple interest for 1 year.
Using the simple interest formula:
I = P * r * t
Where:
I = interest earned
P = principal amount
r = annual interest rate (as a decimal)
t = number of years
I = B * 0.10 * 1
I = B * 0.10
So, the total amount received by B is:
Total = B + I
Total = B + (B * 0.10)
Total = B(1 + 0.10)
Since the total amount received by both A and B is equal, we can set up the equation:
34,617 = B(1 + 0.10)
34,617 = B * 1.10
Solving for B:
B = 34,617 / 1.10
B ≈ $31,470.91
Therefore, B invested approximately $31,470.91 in the scheme.
A invests $22,000 in a bank at 4% interest compounded semi-annually for 11.6 years.
To find:
The amount of money B invested.
Calculating the amount received by A:
We can use the compound interest formula to calculate the amount received by A at the end of 6 years.
The formula for compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
Plugging in the values:
P = $22,000
r = 4% = 0.04
n = 2 (semi-annually compounded)
t = 11.6 years
A = 22000(1 + 0.04/2)^(2 * 11.6)
A = 22000(1 + 0.02)^(23.2)
A = 22000(1.02)^(23.2)
A = 22000 * 1.5735
A = $34,617
Calculating the amount received by B:
Let's assume B invested an amount x in the same scheme for 5 years.
Using the same compound interest formula, we can calculate the amount received by B at the end of 5 years.
P = x
r = 4% = 0.04
n = 2 (semi-annually compounded)
t = 5 years
B = x(1 + 0.04/2)^(2 * 5)
B = x(1 + 0.02)^(10)
B = x(1.02)^(10)
After 5 years, B withdraws the amount and invests it in another bank at 10% simple interest for 1 year.
Using the simple interest formula:
I = P * r * t
Where:
I = interest earned
P = principal amount
r = annual interest rate (as a decimal)
t = number of years
I = B * 0.10 * 1
I = B * 0.10
So, the total amount received by B is:
Total = B + I
Total = B + (B * 0.10)
Total = B(1 + 0.10)
Since the total amount received by both A and B is equal, we can set up the equation:
34,617 = B(1 + 0.10)
34,617 = B * 1.10
Solving for B:
B = 34,617 / 1.10
B ≈ $31,470.91
Therefore, B invested approximately $31,470.91 in the scheme.
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A invests 22000 in a bank at 4% interest compounded semi-annually for11. 6 years. B invests some money in the same scheme for 5 years, theninvests in another bank at 10% simple interest for 1 year. If the amountreceived by both at the end of 6 years was equal, how much money didB invest?
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A invests 22000 in a bank at 4% interest compounded semi-annually for11. 6 years. B invests some money in the same scheme for 5 years, theninvests in another bank at 10% simple interest for 1 year. If the amountreceived by both at the end of 6 years was equal, how much money didB invest? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A invests 22000 in a bank at 4% interest compounded semi-annually for11. 6 years. B invests some money in the same scheme for 5 years, theninvests in another bank at 10% simple interest for 1 year. If the amountreceived by both at the end of 6 years was equal, how much money didB invest? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A invests 22000 in a bank at 4% interest compounded semi-annually for11. 6 years. B invests some money in the same scheme for 5 years, theninvests in another bank at 10% simple interest for 1 year. If the amountreceived by both at the end of 6 years was equal, how much money didB invest?.
A invests 22000 in a bank at 4% interest compounded semi-annually for11. 6 years. B invests some money in the same scheme for 5 years, theninvests in another bank at 10% simple interest for 1 year. If the amountreceived by both at the end of 6 years was equal, how much money didB invest? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A invests 22000 in a bank at 4% interest compounded semi-annually for11. 6 years. B invests some money in the same scheme for 5 years, theninvests in another bank at 10% simple interest for 1 year. If the amountreceived by both at the end of 6 years was equal, how much money didB invest? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A invests 22000 in a bank at 4% interest compounded semi-annually for11. 6 years. B invests some money in the same scheme for 5 years, theninvests in another bank at 10% simple interest for 1 year. If the amountreceived by both at the end of 6 years was equal, how much money didB invest?.
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