Find the C.I on Rs. 6000 at the rate of interest 5% for 3 years, compounded yearly.

Answer

To find the compound interest (C.I) on Rs. 6000 at a rate of 5% for 3 years, compounded yearly, we can follow these steps:

### Step 1: Identify the given values
- Principal (P) = Rs. 6000
- Rate of interest (R) = 5% per annum
- Time (T) = 3 years

**Hint:** Write down all the values you have from the question to keep track of them.

### Step 2: Convert the percentage rate into a decimal
To use the formula for compound interest, we need to convert the percentage into a decimal:
- R = 5% = 5/100 = 0.05

**Hint:** Remember that to convert a percentage to a decimal, divide by 100.

### Step 3: Use the formula for compound interest
The formula for compound interest is:
\[ A = P \left(1 + \frac{R}{n}\right)^{nT} \]
Where:
- A = the amount after time T
- P = principal amount
- R = annual interest rate (in decimal)
- n = number of times interest is compounded per year
- T = time in years

In this case, since the interest is compounded yearly, n = 1. Thus, the formula simplifies to:
\[ A = P (1 + R)^T \]

**Hint:** Make sure you understand the formula and what each variable represents.

### Step 4: Substitute the values into the formula
Substituting the known values into the formula:
\[ A = 6000 \left(1 + 0.05\right)^3 \]
\[ A = 6000 \left(1.05\right)^3 \]

**Hint:** Always double-check that you are substituting the correct values.

### Step 5: Calculate \( (1.05)^3 \)
Now, we need to calculate \( (1.05)^3 \):
\[ (1.05)^3 = 1.157625 \]

**Hint:** You can use a calculator for this step to ensure accuracy.

### Step 6: Calculate the total amount (A)
Now, substitute back to find A:
\[ A = 6000 \times 1.157625 \]
\[ A = 6945.75 \]

**Hint:** Keep track of your calculations to avoid mistakes.

### Step 7: Calculate the compound interest (C.I)
Now, to find the compound interest, subtract the principal from the total amount:
\[ C.I = A - P \]
\[ C.I = 6945.75 - 6000 \]
\[ C.I = 945.75 \]

**Hint:** Remember that the compound interest is the total amount earned minus the principal.

### Final Answer
The compound interest on Rs. 6000 at the rate of 5% for 3 years, compounded yearly, is Rs. 945.75.

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