Amin borrowed some money from Vishwas. The rate of interest for first two years is 8% p.a., for the next three years is 11 % p.a. and for the period beyond 5 years 14% p.a. Vishwas got an amount of 10920 as an interest at the end of eight years. Then what amount was borrowed by Amin’?

Options

A. 12000
B. 15000
C. 1400
D. None of these

Answer

To solve the problem step by step, we will calculate the total interest earned by Vishwas over the 8 years, based on the different interest rates for different periods. We will then use that information to find out the principal amount borrowed by Amin.

### Step 1: Define the Principal Amount
Let the principal amount borrowed by Amin be \( P \).

### Step 2: Calculate Interest for the First 2 Years
The interest rate for the first 2 years is 8% per annum.
The interest for the first 2 years can be calculated using the formula for simple interest:
\[ \text{Interest} = P \times \frac{8}{100} \times 2 = \frac{16P}{100} = 0.16P \]

### Step 3: Calculate Interest for the Next 3 Years
The interest rate for the next 3 years is 11% per annum.
The interest for these 3 years is:
\[ \text{Interest} = P \times \frac{11}{100} \times 3 = \frac{33P}{100} = 0.33P \]

### Step 4: Calculate Interest for the Last 3 Years
The interest rate for the remaining 3 years (beyond 5 years) is 14% per annum.
The interest for these 3 years is:
\[ \text{Interest} = P \times \frac{14}{100} \times 3 = \frac{42P}{100} = 0.42P \]

### Step 5: Total Interest Over 8 Years
Now, we can add up all the interests calculated:
\[ \text{Total Interest} = 0.16P + 0.33P + 0.42P = (0.16 + 0.33 + 0.42)P = 0.91P \]

### Step 6: Set Up the Equation
According to the problem, the total interest earned by Vishwas at the end of 8 years is Rs. 10,920. Therefore, we can set up the equation:
\[ 0.91P = 10920 \]

### Step 7: Solve for Principal Amount
To find \( P \), we divide both sides of the equation by 0.91:
\[ P = \frac{10920}{0.91} = 12000 \]

### Conclusion
Thus, the amount borrowed by Amin is Rs. 12,000.

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