The compound interest on `Rs. 6,000` at `10%` per annum for `1(1)/2` years, when the interest being compounded annually, is

Options

A. `Rs.910`
B. `Rs. 870`
C. `Rs. 930`
D. `Rs.900`

Answer

To find the compound interest on Rs. 6,000 at an interest rate of 10% per annum for 1.5 years, we can follow these steps:

### Step 1: Identify the principal amount and the rate of interest.
- Principal (P) = Rs. 6,000
- Rate of interest (R) = 10% per annum

**Hint:** The principal is the initial amount of money, and the rate of interest is the percentage at which the money grows.

### Step 2: Break down the time period into years.
- Time (T) = 1.5 years = 1 year + 0.5 years

**Hint:** It's useful to separate the time into whole years and fractions for easier calculations.

### Step 3: Calculate the compound interest for the first year.
- For the first year, the interest is calculated on the principal amount.
- Interest for the first year = P × R × T = 6000 × 10/100 × 1 = Rs. 600

**Hint:** Remember that for the first year, you calculate the interest on the original principal.

### Step 4: Calculate the amount after the first year.
- Amount after 1 year = Principal + Interest = 6000 + 600 = Rs. 6,600

**Hint:** The amount after the first year is the sum of the principal and the interest earned.

### Step 5: Calculate the compound interest for the next half year.
- For the next half year, the interest is calculated on the new amount (Rs. 6,600).
- Rate for half a year = 10% / 2 = 5%
- Interest for 0.5 years = Amount × Rate × Time = 6600 × 5/100 × 0.5 = Rs. 165

**Hint:** When calculating interest for a fraction of a year, adjust the rate accordingly.

### Step 6: Calculate the total interest earned.
- Total Compound Interest = Interest for the first year + Interest for the half year
- Total Compound Interest = 600 + 165 = Rs. 765

**Hint:** The total compound interest is the sum of the interest earned in each period.

### Step 7: Final Answer
The compound interest on Rs. 6,000 at 10% per annum for 1.5 years is Rs. 765.

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