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A sum of money becomes Rs 8352 in 2 years and Rs 8928 in 3 years . Find the principal and the rate of interest?
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A sum of money becomes Rs 8352 in 2 years and Rs 8928 in 3 years . Fin...
Given:
- The sum of money becomes Rs 8352 in 2 years.
- The sum of money becomes Rs 8928 in 3 years.

To find:
- The principal amount.
- The rate of interest.

Formula:
The formula to calculate compound interest is:

A = P(1 + r/n)^(nt)

Where:
A = Final amount
P = Principal amount
r = Annual interest rate (in decimal form)
n = Number of times that interest is compounded per year
t = Number of years

Assumptions:
- The interest is compounded annually.

Solution:
We can solve this problem using the given information and the compound interest formula.

Step 1: Calculate the compound interest for 2 years.
- Rs 8352 = P(1 + r)^2

Step 2: Calculate the compound interest for 3 years.
- Rs 8928 = P(1 + r)^3

Step 3: Solve the above equations to find P and r.
- Divide the equation obtained in Step 2 by the equation obtained in Step 1:
(Rs 8928 / Rs 8352) = (P(1 + r)^3) / (P(1 + r)^2)

Step 4: Simplify the equation.
- Cancel out the common terms:
(8928 / 8352) = (1 + r)^3 / (1 + r)^2

- Simplify the equation further:
(1064 / 4176) = (1 + r)

Step 5: Solve for r.
- Subtract 1 from both sides of the equation:
(1064 / 4176) - 1 = r

- Simplify the equation:
r = (1064 - 4176) / 4176

- Calculate the value of r:
r = -3112 / 4176
r = -0.745

Step 6: Substitute the value of r into one of the initial equations to find P.
- Use the equation obtained in Step 1:
Rs 8352 = P(1 + (-0.745))^2

- Simplify the equation:
Rs 8352 = P(0.255)^2

- Calculate the value of P:
P = 8352 / (0.255)^2
P = 8352 / 0.065025
P = Rs 128246.15

Conclusion:
The principal amount is Rs 128246.15 and the rate of interest is -0.745 (which is -74.5%).
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A sum of money becomes Rs 8352 in 2 years and Rs 8928 in 3 years . Find the principal and the rate of interest?
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A sum of money becomes Rs 8352 in 2 years and Rs 8928 in 3 years . Find the principal and the rate of interest? for Class 7 2024 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about A sum of money becomes Rs 8352 in 2 years and Rs 8928 in 3 years . Find the principal and the rate of interest? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A sum of money becomes Rs 8352 in 2 years and Rs 8928 in 3 years . Find the principal and the rate of interest?.
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