Find the compound interest on Rs. 15625 for 9 months at 16% per annum compounded quarterly.

Answer

To find the compound interest on Rs. 15625 for 9 months at 16% per annum compounded quarterly, we can follow these steps:

### Step 1: Identify the principal amount, rate of interest, and time period.
- Principal (P) = Rs. 15625
- Annual Rate of Interest (R) = 16%
- 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 Rate (r) = R / 4 = 16% / 4 = 4%

### Step 3: Convert the time period into years.
Since the interest is compounded quarterly, we need to express the time in years:
- Time in years (T) = 9 months = 9/12 = 0.75 years

### Step 4: Calculate the number of compounding periods.
Since the interest is compounded quarterly, we multiply the time in years by 4:
- Number of compounding periods (n) = 4 * T = 4 * 0.75 = 3

### Step 5: Use the compound interest formula to calculate the total amount.
The formula for compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^n \]
Where:
- A = Total amount after interest
- P = Principal amount
- r = Quarterly interest rate
- n = Number of compounding periods

Substituting the values:
\[ A = 15625 \left(1 + \frac{4}{100}\right)^3 \]
\[ A = 15625 \left(1 + 0.04\right)^3 \]
\[ A = 15625 \left(1.04\right)^3 \]

### Step 6: Calculate \( (1.04)^3 \).
Calculating \( (1.04)^3 \):
\[ (1.04)^3 = 1.124864 \]

### Step 7: Calculate the total amount (A).
Now, substitute back into the formula:
\[ A = 15625 \times 1.124864 \]
\[ A \approx 17576 \]

### Step 8: Calculate the compound interest (CI).
Compound Interest (CI) is calculated as:
\[ CI = A - P \]
\[ CI = 17576 - 15625 \]
\[ CI = 1951 \]

### Final Answer:
The compound interest on Rs. 15625 for 9 months at 16% per annum compounded quarterly is Rs. 1951.

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