A private finance company A claims to be lending money at simple interest. But the company includes the interest every 6 months for calculating principal. If company A is charging an interest of 10%, the effective rate of interest after 1 yr becomes

Options

A. 0.1025
B. 0.125
C. 0.1125
D. 0.1075

Answer

To solve the problem, we need to determine the effective rate of interest charged by company A after one year, given that they are compounding the interest every 6 months at a nominal rate of 10% per annum.

### Step-by-Step Solution

**Step 1: Understand the interest rate and compounding frequency.**
- The nominal interest rate is 10% per annum.
- The interest is compounded every 6 months, which means there are 2 compounding periods in a year.

**Hint:** Remember that when interest is compounded, the effective interest rate can be different from the nominal rate.

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**Step 2: Calculate the interest rate per compounding period.**
- Since the interest is compounded every 6 months, we divide the annual interest rate by the number of compounding periods in a year.
- Interest rate per 6 months = 10% / 2 = 5%.

**Hint:** Always divide the annual interest rate by the number of compounding periods to find the rate for each period.

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**Step 3: Calculate the total amount after 1 year.**
- If we assume a principal amount (P), the amount after the first 6 months will be:
- Amount after 6 months = P + (5% of P) = P + 0.05P = 1.05P.

- For the next 6 months, we calculate the interest on the new principal (1.05P):
- Amount after 1 year = 1.05P + (5% of 1.05P) = 1.05P + 0.0525P = 1.1025P.

**Hint:** When calculating the amount after compounding, always apply the interest to the new principal.

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**Step 4: Determine the effective interest rate.**
- The effective interest earned over the year is:
- Effective Interest = Total Amount - Principal = 1.1025P - P = 0.1025P.

- To find the effective rate of interest, we express the effective interest as a percentage of the principal:
- Effective Rate = (Effective Interest / Principal) × 100 = (0.1025P / P) × 100 = 10.25%.

**Hint:** To find the effective rate, always compare the effective interest earned to the original principal.

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**Final Answer:**
The effective rate of interest after 1 year becomes **10.25%**.