Rs 770 was paid in 5 years, in 5 annual install ment. If the rate of SI is 5% per annum find out the amont of each installment.

Options

A. Rs 140
B. Rs 160
C. Rs 170
D. Rs 180

Answer

To find the amount of each installment when Rs 770 is paid in 5 years in 5 annual installments at a simple interest rate of 5% per annum, we can follow these steps:

### Step 1: Understand the Total Amount and Installments
The total amount paid over 5 years is Rs 770. This amount includes both the principal and the interest accrued over the 5 years.

### Step 2: Identify the Variables
- Total Amount (A) = Rs 770
- Rate of Interest (R) = 5% per annum
- Time (T) = 5 years
- Number of Installments (N) = 5

### Step 3: Calculate the Total Interest
The formula for Simple Interest (SI) is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Where:
- P = Principal amount
- R = Rate of interest
- T = Time in years

Let the principal amount be \( P \). The total amount paid (A) can be expressed as:
\[ A = P + \text{SI} \]
Substituting the SI formula:
\[ A = P + \frac{P \times R \times T}{100} \]
This can be rewritten as:
\[ A = P \left(1 + \frac{R \times T}{100}\right) \]

### Step 4: Substitute the Known Values
Substituting the known values into the equation:
\[ 770 = P \left(1 + \frac{5 \times 5}{100}\right) \]
\[ 770 = P \left(1 + \frac{25}{100}\right) \]
\[ 770 = P \left(1 + 0.25\right) \]
\[ 770 = P \times 1.25 \]

### Step 5: Solve for Principal (P)
Now, solve for \( P \):
\[ P = \frac{770}{1.25} \]
\[ P = 616 \]

### Step 6: Calculate the Total Interest
Now we can calculate the total interest:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
\[ \text{SI} = \frac{616 \times 5 \times 5}{100} \]
\[ \text{SI} = \frac{15400}{100} \]
\[ \text{SI} = 154 \]

### Step 7: Calculate the Total Amount Paid
Now we can find the total amount paid:
\[ A = P + \text{SI} \]
\[ A = 616 + 154 \]
\[ A = 770 \] (which confirms our calculation)

### Step 8: Find the Amount of Each Installment
Since the total amount paid is Rs 770 over 5 installments, the amount of each installment (I) is:
\[ I = \frac{A}{N} \]
\[ I = \frac{770}{5} \]
\[ I = 154 \]

### Final Answer
The amount of each installment is Rs 154.

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