A perseon takes loan of Rs 4,000 on the condition that he would pay it in the monthly instalment of Rs 500. He has to pay interest at the rate of 6 % on the outstanding balances, then find out the average rate of interset received by the creditor.

Options

A. `3(3)/(8)` % Percent Per annum
B. `2(3)/(8)` % Percent Per annum
C. `4(3)/(8)` % Percent Per annum
D. `3(1)/(8)` % Percent Per annum

Answer

To solve the problem step by step, we will calculate the average rate of interest received by the creditor based on the loan amount, monthly installments, and interest rate on the outstanding balance.

### Step 1: Understand the Loan Details
- Principal (Loan Amount) = Rs 4000
- Monthly Installment = Rs 500
- Interest Rate = 6% per annum = 0.5% per month (6% / 12)

### Step 2: Calculate the Interest for Each Month
1. **First Month:**
- Outstanding Balance = Rs 4000
- Interest = 0.5% of 4000 = (0.5/100) * 4000 = Rs 20

2. **Second Month:**
- Outstanding Balance after first payment = 4000 - 500 = Rs 3500
- Interest = 0.5% of 3500 = (0.5/100) * 3500 = Rs 17.5

3. **Third Month:**
- Outstanding Balance after second payment = 3500 - 500 = Rs 3000
- Interest = 0.5% of 3000 = (0.5/100) * 3000 = Rs 15

4. **Fourth Month:**
- Outstanding Balance after third payment = 3000 - 500 = Rs 2500
- Interest = 0.5% of 2500 = (0.5/100) * 2500 = Rs 12.5

5. **Fifth Month:**
- Outstanding Balance after fourth payment = 2500 - 500 = Rs 2000
- Interest = 0.5% of 2000 = (0.5/100) * 2000 = Rs 10

6. **Sixth Month:**
- Outstanding Balance after fifth payment = 2000 - 500 = Rs 1500
- Interest = 0.5% of 1500 = (0.5/100) * 1500 = Rs 7.5

7. **Seventh Month:**
- Outstanding Balance after sixth payment = 1500 - 500 = Rs 1000
- Interest = 0.5% of 1000 = (0.5/100) * 1000 = Rs 5

8. **Eighth Month:**
- Outstanding Balance after seventh payment = 1000 - 500 = Rs 500
- Interest = 0.5% of 500 = (0.5/100) * 500 = Rs 2.5

9. **Ninth Month:**
- Outstanding Balance after eighth payment = 500 - 500 = Rs 0
- Interest = 0.5% of 0 = Rs 0

### Step 3: Calculate Total Interest Paid
Total Interest = 20 + 17.5 + 15 + 12.5 + 10 + 7.5 + 5 + 2.5 + 0 = Rs 90

### Step 4: Calculate Average Rate of Interest
To find the average rate of interest, we can use the formula for Simple Interest:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Where:
- SI = Total Interest = Rs 90
- P = Principal = Rs 4000
- R = Average Rate of Interest (unknown)
- T = Time in years = 8 months = \(\frac{8}{12}\) years

Rearranging the formula to find R:
\[ R = \frac{SI \times 100}{P \times T} \]
Substituting the values:
\[ R = \frac{90 \times 100}{4000 \times \frac{8}{12}} \]
\[ R = \frac{9000}{4000 \times \frac{2}{3}} \]
\[ R = \frac{9000 \times 3}{8000} \]
\[ R = \frac{27000}{8000} \]
\[ R = 3.375 \]

### Final Result
The average rate of interest received by the creditor is **3.375%**.

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