Rs. 1720 to be paid in 4 equal installments in 4 years. Find each intallment if rate of interest is 5% per annum.

Answer

To find the amount of each installment when Rs. 1720 is to be paid in 4 equal installments over 4 years at an interest rate of 5% per annum, we can follow these steps:

### Step 1: Understand the Problem
We need to pay Rs. 1720 in 4 equal installments over 4 years with an interest rate of 5% per annum.

**Hint:** Identify the total amount to be paid and the number of installments.

### Step 2: Calculate the Total Amount of Interest
The interest will be calculated on each installment based on the time it remains unpaid. The first installment will not incur any interest for the first year, the second installment will incur interest for 1 year, the third for 2 years, and the fourth for 3 years.

**Hint:** Remember that the interest for each installment depends on how long it is outstanding.

### Step 3: Set Up the Equation
Let the amount of each installment be \( x \). The total amount paid at the end of 4 years will be the sum of the installments plus the interest on each installment.

The total amount can be expressed as:
\[ x + \left( x + \frac{5}{100} \cdot x \right) + \left( x + 2 \cdot \frac{5}{100} \cdot x \right) + \left( x + 3 \cdot \frac{5}{100} \cdot x \right) = 1720 \]

This simplifies to:
\[ x + x + 0.05x + x + 0.10x + x + 0.15x = 1720 \]

Combining like terms gives:
\[ 4x + (0.05 + 0.10 + 0.15)x = 1720 \]
\[ 4x + 0.30x = 1720 \]
\[ 4.30x = 1720 \]

**Hint:** Combine like terms carefully to simplify the equation.

### Step 4: Solve for \( x \)
Now, we can solve for \( x \):
\[ x = \frac{1720}{4.30} \]

Calculating this gives:
\[ x = 400 \]

**Hint:** Perform the division to find the value of each installment.

### Step 5: Conclusion
Each installment is Rs. 400.

**Final Answer:** Each installment is Rs. 400.