Avinash borrowed $$ ₹ 32,000 $$ from his friend Gaurav at the rate of $$ 8 \% $$ per annum simple interest for 3 years, He lent this money to Vivek at the same rate but compounded annually. Find hais gafter 3 years. Kamala borrowed $$ ₹ 36,400 $$ from a Bank to buy a scooter at a rate of $$ 15 \% $$ p.a. compounded yearly. What

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### **Problem 1: Avinash's Gain Calculation**

**Given:**
- **Principal (P):** ₹32,000
- **Interest Rate (R):** 8% per annum
- **Time (T):** 3 years

**Avinash's Borrowing (Simple Interest):**

Avinash borrows ₹32,000 from Gaurav at **simple interest (SI)**.

The formula for Simple Interest is:
$$
\text{SI} = \frac{P \times R \times T}{100}
$$

Calculating the interest:
$$
\text{SI} = \frac{32,000 \times 8 \times 3}{100} = \frac{768,000}{100} = ₹7,680
$$

**Total Amount to be Repaid to Gaurav:**
$$
\text{Total} = P + \text{SI} = 32,000 + 7,680 = ₹39,680
$$

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**Avinash's Lending (Compound Interest):**

Avinash lends the same ₹32,000 to Vivek at **compound interest (CI)** annually at the same rate.

The formula for Compound Interest is:
$$
A = P \times (1 + \frac{R}{100})^T
$$

Calculating the amount after 3 years:
$$
A = 32,000 \times \left(1 + \frac{8}{100}\right)^3 = 32,000 \times (1.08)^3
$$
$$
(1.08)^3 = 1.259712
$$
$$
A = 32,000 \times 1.259712 \approx ₹40,310.78
$$

**Total Interest Received from Vivek:**
$$
\text{Interest} = A - P = 40,310.78 - 32,000 = ₹8,310.78
$$

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**Avinash's Net Gain:**
$$
\text{Net Gain} = \text{Interest Received} - \text{Interest Paid} = 8,310.78 - 7,680 = ₹630.78
$$

**Approximate Net Gain:** ₹631 after 3 years.

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### **Problem 2: Kamala's Loan Details**

**Given:**
- **Principal (P):** ₹36,400
- **Interest Rate (R):** 15% per annum
- **Compounding:** Yearly

**Incomplete Information:**
It seems like the question for Kamala is incomplete. To provide a comprehensive answer, additional information is needed, such as:
- **Time Period (T):** Number of years for the loan.
- **Specific Query:** Are you asking for the total amount to be repaid, the total interest, monthly installments, etc.?

**Please provide the complete question or the missing details**, and I'll be happy to assist you further!

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Avinash borrows ₹32,000 at 8% simple interest for 3 years, paying ₹7,680 in interest, totaling ₹39,680. He lends the same amount to Vivek at 8% compound interest annually, earning approximately ₹8,310.78 after 3 years. His net gain is ₹630.78. Kamala borrowed ₹36,400 at 15% compounded yearly, but the time period and specific details are missing. Please provide complete information for a full solution.

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