Question

Calculate the compound interest on ₹1000 for a period of one year at the rate 10% per annum, if interest is compounded quarterly?

• A. ₹101.81
• B. ₹102.81
• C. ₹103.81
• D. ₹104.18

Hint:

For compound interest, always use the formula \( A = P \left(1 + \frac{r}{100n}\right)^{nt} \) and ensure you use the correct values for the number of periods per year when compounding is more frequent than annually.

Answer 1

The Correct Option is C

We are given the following:
Principal (\( P \)) = ₹1000
Rate of interest (\( r \)) = 10% per annum
Time (\( t \)) = 1 year
Interest is compounded quarterly, so the number of times interest is compounded per year (\( n \)) = 4
We will use the compound interest formula: \[ A = P \left( 1 + \frac{r}{100n} \right)^{nt} \] Step 1: Substitute the given values into the formula.
Substitute \( P = 1000 \), \( r = 10% \), \( n = 4 \) (quarterly compounding), and \( t = 1 \) year into the formula: \[ A = 1000 \left( 1 + \frac{10}{100 \times 4} \right)^{4 \times 1} \] Simplifying the expression: \[ A = 1000 \left( 1 + \frac{1}{40} \right)^4 = 1000 \left( \frac{41}{40} \right)^4 \]

Step 2: Calculate the value of \( \left( \frac{41}{40} \right)^4 \).
Now, calculate \( \left( \frac{41}{40} \right)^4 \): \[ \left( \frac{41}{40} \right)^4 \approx 1.103812 \]

Step 3: Find the amount \( A \). Now, multiply by 1000 to find \( A \): \[ A = 1000 \times 1.103812 = 1103.81 \] Step 4: Calculate the compound interest. The compound interest \( CI \) is the difference between the total amount \( A \) and the principal \( P \): \[ CI = A - P = 1103.81 - 1000 = ₹103.81 \] Thus, the compound interest is ₹103.81.