A sum of rs.40080 was borrowed at `8(3)/(4)%` per annum compound interest and paid back in two years in two equal installments. What was the amount of each intstallment ?

Options

A. ₹22707
B. ₹ 21807
C. ₹ 23805
D. ₹24000

Answer

To solve the problem of finding the amount of each installment for a sum of Rs. 40080 borrowed at an interest rate of 8(3/4)% per annum compounded annually, we can follow these steps:

### Step 1: Convert the interest rate to a decimal
The interest rate given is 8(3/4)%, which can be converted to an improper fraction:
- 8(3/4)% = 8.75% = 8.75/100 = 0.0875

### Step 2: Determine the total amount after 2 years
To find the total amount after 2 years using compound interest, we use the formula:
\[ A = P(1 + r)^n \]
Where:
- \( A \) = total amount after n years
- \( P \) = principal amount (Rs. 40080)
- \( r \) = rate of interest (0.0875)
- \( n \) = number of years (2)

Substituting the values:
\[ A = 40080(1 + 0.0875)^2 \]
\[ A = 40080(1.0875)^2 \]
\[ A = 40080 \times 1.18265625 \]
\[ A \approx 47353.59 \]

### Step 3: Calculate the total amount to be paid back
The total amount to be paid back after 2 years is approximately Rs. 47353.59.

### Step 4: Determine the value of each installment
Since the total amount is paid back in two equal installments, we divide the total amount by 2:
\[ \text{Installment} = \frac{47353.59}{2} \]
\[ \text{Installment} \approx 23676.80 \]

### Final Answer
The amount of each installment is approximately Rs. 23676.80.

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