Question

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

• A. 8
• B. 110
• C. 120
• D. 103

Hint:

For compound interest, remember to adjust the rate and time based on the frequency of compounding periods (quarterly, monthly, etc.).

Answer 1

The Correct Option is D

We are given:
Principal amount \( P = 1000 \)
Rate of interest \( r = 10% \) per annum
Time \( t = 1 \) year
The interest is compounded quarterly, so the number of compounding periods per year \( n = 4 \)
Step 1: The formula for compound interest is: \[ A = P \left( 1 + \frac{r}{100n} \right)^{nt} \] where:
\( P \) is the principal amount,
\( r \) is the annual rate of interest,
\( n \) is the number of times interest is compounded per year,
\( t \) is the number of years.


Step 2: Substitute the known values: \[ A = 1000 \left( 1 + \frac{10}{100 \times 4} \right)^{4 \times 1} = 1000 \left( 1 + 0.025 \right)^4 = 1000 \left( 1.025 \right)^4. \]

Step 3: Calculate \( (1.025)^4 \): \[ (1.025)^4 = 1.103812. \]

Step 4: Now, calculate \( A \): \[ A = 1000 \times 1.103812 = 1103.812. \]

Step 5: The compound interest is given by: \[ \text{Compound Interest} = A - P = 1103.812 - 1000 = 103.812. \]