The compound interest on Rs. 12000 for 9 months at 20% per annum, interest being compounded quarterly, is :

Answer

To find the compound interest on Rs. 12000 for 9 months at a rate of 20% per annum, compounded quarterly, we can follow these steps:

### Step 1: Identify the principal amount, rate of interest, and time period.
- Principal (P) = Rs. 12000
- Annual interest rate (R) = 20%
- Time (T) = 9 months

### Step 2: Convert the annual interest rate to a quarterly interest rate.
Since the interest is compounded quarterly, we need to divide the annual rate by 4.
- Quarterly interest rate = \( \frac{20\%}{4} = 5\% \)

### Step 3: Convert the time period from months to quarters.
Since there are 3 months in a quarter, we convert 9 months to quarters.
- Time in quarters = \( \frac{9 \text{ months}}{3 \text{ months/quarter}} = 3 \text{ quarters} \)

### Step 4: Use the compound interest formula.
The formula for compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^n \]
Where:
- \( A \) = Amount after time \( T \)
- \( P \) = Principal amount
- \( r \) = Rate of interest per period
- \( n \) = Number of compounding periods

Substituting the values:
- \( P = 12000 \)
- \( r = 5 \) (quarterly rate)
- \( n = 3 \) (number of quarters)

\[ A = 12000 \left(1 + \frac{5}{100}\right)^3 \]

### Step 5: Calculate the amount \( A \).
First, calculate \( 1 + \frac{5}{100} = 1 + 0.05 = 1.05 \).
Now calculate \( (1.05)^3 \):
\[ (1.05)^3 = 1.157625 \]
Now substitute this back into the amount formula:
\[ A = 12000 \times 1.157625 = 13891.50 \]

### Step 6: Calculate the compound interest.
Compound Interest (CI) is given by:
\[ CI = A - P \]
Substituting the values:
\[ CI = 13891.50 - 12000 = 1891.50 \]

### Final Answer:
The compound interest on Rs. 12000 for 9 months at 20% per annum, compounded quarterly, is Rs. 1891.50.

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