If the simple interest on a certain sum of money for 3 yrs at 5% is Rs 150, find the corresponding CI.
(a)157.625
(b)190
(c)200
(d)153.5

Answer

To solve the problem of finding the corresponding compound interest (CI) given the simple interest (SI) for a certain sum of money, we can follow these steps:

### Step 1: Understand the Given Information
We are given:
- Simple Interest (SI) = Rs. 150
- Rate of Interest (R) = 5%
- Time (T) = 3 years

### Step 2: Use the Simple Interest Formula to Find Principal (P)
The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Substituting the known values:
\[ 150 = \frac{P \times 5 \times 3}{100} \]

### Step 3: Rearrange the Formula to Solve for Principal (P)
Rearranging the equation gives us:
\[ 150 = \frac{15P}{100} \]
Multiplying both sides by 100:
\[ 15000 = 15P \]
Now, divide both sides by 15:
\[ P = \frac{15000}{15} = 1000 \]

### Step 4: Calculate Compound Interest (CI)
To find the CI, we can use the formula:
\[ CI = P \left(1 + \frac{R}{100}\right)^T - P \]
Substituting the values we found:
\[ CI = 1000 \left(1 + \frac{5}{100}\right)^3 - 1000 \]
This simplifies to:
\[ CI = 1000 \left(1.05\right)^3 - 1000 \]

### Step 5: Calculate \( (1.05)^3 \)
Calculating \( (1.05)^3 \):
\[ (1.05)^3 = 1.157625 \]
Now substituting back into the CI formula:
\[ CI = 1000 \times 1.157625 - 1000 \]
\[ CI = 1157.625 - 1000 = 157.625 \]

### Step 6: Final Answer
Thus, the corresponding compound interest (CI) is:
\[ \text{CI} = Rs. 157.625 \]

### Conclusion
The correct answer is (a) 157.625.

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