In what time will 8,000, at 3% per annum, produce the same Interest as 6 000 does In 5 years at 4 % simple interest?

Options

A. 5 years
B. 6 years
C. 3 years
D. 4 years

Answer

To solve the problem step by step, we need to find out how long it will take for an investment of 8,000 at an interest rate of 3% per annum to generate the same interest as an investment of 6,000 at an interest rate of 4% over 5 years.

### Step 1: Calculate the Simple Interest for 6,000 at 4% for 5 Years
The formula for Simple Interest (SI) is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Where:
- \( P \) = Principal amount
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

For the first investment:
- \( P = 6000 \)
- \( R = 4 \% \)
- \( T = 5 \)

Substituting the values into the formula:
\[ \text{SI} = \frac{6000 \times 4 \times 5}{100} \]
\[ \text{SI} = \frac{120000}{100} \]
\[ \text{SI} = 1200 \]

### Step 2: Set Up the Equation for 8,000 at 3% to Find Time
Now, we need to find the time \( T \) for the second investment of 8,000 at 3% to generate the same interest of 1200.

Using the same formula for Simple Interest:
For the second investment:
- \( P = 8000 \)
- \( R = 3 \% \)
- \( T = ? \)

Setting up the equation:
\[ 1200 = \frac{8000 \times 3 \times T}{100} \]

### Step 3: Solve for T
Rearranging the equation to solve for \( T \):
\[ 1200 = \frac{8000 \times 3 \times T}{100} \]
\[ 1200 = 240 \times T \]
\[ T = \frac{1200}{240} \]
\[ T = 5 \]

### Conclusion
The time it will take for 8,000 at 3% per annum to produce the same interest as 6,000 does in 5 years at 4% simple interest is **5 years**.

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