A certain sum of money, invested for 5 years at 8% p.a. simple interest, earns an interest of Rs. 12,000. Find :
(i) the sum of money.
(ii) the compound interest earned by this money in two years at 10% p.a. compound interest.

Answer

To solve the problem step by step, we will break it down into two parts as required:

### Part (i): Finding the Sum of Money (Principal)

1. **Identify the Formula for Simple Interest**:
The formula for Simple Interest (SI) is given by:
\[ SI = \frac{P \times R \times T}{100} \]
where:
- \(SI\) = Simple Interest
- \(P\) = Principal (the sum of money)
- \(R\) = Rate of interest per annum
- \(T\) = Time in years

2. **Substitute the Known Values**:
From the question:
- \(SI = 12,000\) (the interest earned)
- \(R = 8\%\) (rate of interest)
- \(T = 5\) years (time period)

Plugging these values into the formula:
\[ 12,000 = \frac{P \times 8 \times 5}{100} \]

3. **Simplify the Equation**:
Rearranging the equation to isolate \(P\):
\[ 12,000 = \frac{40P}{100} \]
\[ 12,000 = \frac{P}{2.5} \]

4. **Multiply Both Sides by 2.5**:
\[ P = 12,000 \times 2.5 \]
\[ P = 30,000 \]

5. **Conclusion for Part (i)**:
The sum of money (Principal) is Rs. 30,000.

### Part (ii): Finding the Compound Interest for 2 Years at 10% p.a.

1. **Identify the Formula for Compound Interest**:
The formula for the amount (A) in compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
where:
- \(A\) = Amount after time \(T\)
- \(P\) = Principal
- \(R\) = Rate of interest per annum
- \(T\) = Time in years

2. **Substitute the Known Values**:
From the previous part, we have:
- \(P = 30,000\)
- \(R = 10\%\)
- \(T = 2\) years

Plugging these values into the formula:
\[ A = 30,000 \left(1 + \frac{10}{100}\right)^2 \]

3. **Calculate the Amount**:
Simplifying the expression:
\[ A = 30,000 \left(1 + 0.1\right)^2 \]
\[ A = 30,000 \left(1.1\right)^2 \]
\[ A = 30,000 \times 1.21 \]
\[ A = 36,300 \]

4. **Calculate the Compound Interest**:
The Compound Interest (CI) is given by:
\[ CI = A - P \]
Substituting the values:
\[ CI = 36,300 - 30,000 \]
\[ CI = 6,300 \]

5. **Conclusion for Part (ii)**:
The compound interest earned by this money in two years at 10% p.a. is Rs. 6,300.

### Summary of Answers:
- (i) The sum of money (Principal) is Rs. 30,000.
- (ii) The compound interest earned in two years at 10% p.a. is Rs. 6,300.