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A certain sum of money invested at the rate of 10% per annum compound interest, interest compounded annually. If the difference between the interest of IIIrd year and the first yeat is $1105. Find the sum invested?
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A certain sum of money invested at the rate of 10% per annum compound ...
For Annual compound intrest,Amount A at the end of n years is given by A =P(1+r)n where, r is rate of intrest expressed as percentage
Rate of intrest on a amount C =c*r where r is rate of intrest expressed as percentage
Let , the invested amount be P
rate of intrest r=10/100=0.1
Intrest of first year = P * 10/100 = 0.1P
Amount at the end of second year = A2=
Intrest of third year = A2*0.1
Given , difference between intrest of third year and first year is rs.1105
So, 0.1*P* - 0.1P = 1105
0.1P() = 1105
0.1P(0.21) = 1105
P = Rs.52619
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A certain sum of money invested at the rate of 10% per annum compound ...
Understanding Compound Interest
When money is invested at compound interest, the interest earned in each period is added to the principal for the calculation of interest in the next period. In this case, the interest is compounded annually at a rate of 10%.
Interest Calculation
- First Year Interest (I1): The interest for the first year is calculated on the principal (P) at 10%.
I1 = P × 10% = 0.1P
- Third Year Interest (I3): The interest for the third year is calculated on the amount after two years of compounding.
Amount after 2 years = P(1 + 0.1)^2 = P(1.1)^2 = P × 1.21
I3 = Amount after 2 years × 10% = P × 1.21 × 0.1 = 0.121P
Difference Between Interests
The difference between the interest earned in the third year and the first year is given as $1105.
- Difference Formula:
I3 - I1 = 0.121P - 0.1P = 0.021P
- Setting Up the Equation:
0.021P = 1105
Finding the Principal Amount
To find the sum invested (P), we rearrange the equation:
P = 1105 / 0.021
P = 52,619.05 (approximately)
Conclusion
The sum invested at a 10% compound interest rate, where the difference in interest between the third and first year is $1105, is approximately $52,619.05.
When money is invested at compound interest, the interest earned in each period is added to the principal for the calculation of interest in the next period. In this case, the interest is compounded annually at a rate of 10%.
Interest Calculation
- First Year Interest (I1): The interest for the first year is calculated on the principal (P) at 10%.
I1 = P × 10% = 0.1P
- Third Year Interest (I3): The interest for the third year is calculated on the amount after two years of compounding.
Amount after 2 years = P(1 + 0.1)^2 = P(1.1)^2 = P × 1.21
I3 = Amount after 2 years × 10% = P × 1.21 × 0.1 = 0.121P
Difference Between Interests
The difference between the interest earned in the third year and the first year is given as $1105.
- Difference Formula:
I3 - I1 = 0.121P - 0.1P = 0.021P
- Setting Up the Equation:
0.021P = 1105
Finding the Principal Amount
To find the sum invested (P), we rearrange the equation:
P = 1105 / 0.021
P = 52,619.05 (approximately)
Conclusion
The sum invested at a 10% compound interest rate, where the difference in interest between the third and first year is $1105, is approximately $52,619.05.
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A certain sum of money invested at the rate of 10% per annum compound interest, interest compounded annually. If the difference between the interest of IIIrd year and the first yeat is $1105. Find the sum invested?
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A certain sum of money invested at the rate of 10% per annum compound interest, interest compounded annually. If the difference between the interest of IIIrd year and the first yeat is $1105. Find the sum invested? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about A certain sum of money invested at the rate of 10% per annum compound interest, interest compounded annually. If the difference between the interest of IIIrd year and the first yeat is $1105. Find the sum invested? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A certain sum of money invested at the rate of 10% per annum compound interest, interest compounded annually. If the difference between the interest of IIIrd year and the first yeat is $1105. Find the sum invested?.
A certain sum of money invested at the rate of 10% per annum compound interest, interest compounded annually. If the difference between the interest of IIIrd year and the first yeat is $1105. Find the sum invested? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about A certain sum of money invested at the rate of 10% per annum compound interest, interest compounded annually. If the difference between the interest of IIIrd year and the first yeat is $1105. Find the sum invested? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A certain sum of money invested at the rate of 10% per annum compound interest, interest compounded annually. If the difference between the interest of IIIrd year and the first yeat is $1105. Find the sum invested?.
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