A sum of Rs 1400 becomes Rs 2408 in 8 yrs at simple interest, then find the rate of interest for last 4 yrs,if the interest rate for `1^(st)` 4 yrs is 12% per annum ?.

Options

A. 8%
B. 11%
C. 6.3%
D. 5.9%

Answer

To solve the problem step by step, we will follow the outlined process to find the rate of interest for the last 4 years.

### Step 1: Identify the Given Information
- Principal (P) = Rs 1400
- Amount after 8 years (A) = Rs 2408
- Time (T) = 8 years
- Rate of interest for the first 4 years = 12% per annum

### Step 2: Calculate the Total Interest Earned
The total interest (SI) earned over 8 years can be calculated using the formula:
\[ SI = A - P \]
Substituting the values:
\[ SI = 2408 - 1400 = 1008 \]

### Step 3: Calculate the Interest for the First 4 Years
Using the simple interest formula for the first 4 years:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- P = 1400
- R = 12% (for the first 4 years)
- T = 4

Substituting the values:
\[ SI = \frac{1400 \times 12 \times 4}{100} \]
Calculating this:
\[ SI = \frac{1400 \times 48}{100} = 672 \]

### Step 4: Calculate the Interest for the Last 4 Years
Now, we need to find the interest earned in the last 4 years. We already know the total interest earned in 8 years is 1008, and the interest earned in the first 4 years is 672. Therefore, the interest for the last 4 years (SI_last) is:
\[ SI_{last} = SI_{total} - SI_{first} \]
Substituting the values:
\[ SI_{last} = 1008 - 672 = 336 \]

### Step 5: Calculate the Rate of Interest for the Last 4 Years
Now we will use the simple interest formula again to find the rate of interest (R) for the last 4 years:
\[ SI_{last} = \frac{P \times R \times T}{100} \]
Where:
- SI_last = 336
- P = 1400
- T = 4

Rearranging the formula to find R:
\[ R = \frac{SI_{last} \times 100}{P \times T} \]
Substituting the values:
\[ R = \frac{336 \times 100}{1400 \times 4} \]
Calculating this:
\[ R = \frac{33600}{5600} = 6 \]

### Final Answer
The rate of interest for the last 4 years is **6% per annum**.

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