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A sum of money compounded annually becomes Rs. 625 in 2 years and Rs. 675 in 3 years. The rate of interest per annum is
  • a)
    7%
  • b)
    10%
  • c)
    6%
  • d)
    8%
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
A sum of money compounded annually becomes Rs. 625 in 2 years and Rs. ...
Given:
- The sum of money compounded annually becomes Rs. 625 in 2 years.
- The sum of money compounded annually becomes Rs. 675 in 3 years.

To find:
The rate of interest per annum.

Solution:
Let's assume the principal amount as P and the rate of interest as R%.

Compound Interest Formula:
The formula to calculate the compound interest is:
A = P(1 + R/100)^n

Where:
A = Final amount
P = Principal amount
R = Rate of interest per annum
n = Number of compounding periods

Using the given information:
1) We know that the sum of money becomes Rs. 625 in 2 years.
Using the compound interest formula:
625 = P(1 + R/100)^2

2) We also know that the sum of money becomes Rs. 675 in 3 years.
Using the compound interest formula:
675 = P(1 + R/100)^3

We have two equations with two unknowns (P and R). We can solve these equations simultaneously to find the value of R.

Solving the equations:
1) Divide the second equation by the first equation:
675/625 = (P(1 + R/100)^3) / (P(1 + R/100)^2)
1.08 = (1 + R/100)

2) Subtract 1 from both sides:
0.08 = R/100

3) Multiply both sides by 100:
8 = R

Therefore, the rate of interest per annum is 8%.

Conclusion:
The rate of interest per annum is 8% (option D).
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Community Answer
A sum of money compounded annually becomes Rs. 625 in 2 years and Rs. ...
For a difference of 1 year, CI can be computed as SI. Hence From the 2nd year to the 3rd year, interest earned = (675-650) = Rs.50 on Rs.625
Hence, the rate of interest = 50/625x100 = 8% per annum
Alternative method :
Since the values are for consecutive years,
which is the interest component
1/25 = 4%
2/25 = 8%
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