Raghu borrowed Rs.80,000 at a certain rate of simple interest payable at the end of 7 years. After 2 years, he repaid Rs.60,000 towards the principal and after 5 more years, he repaid Rs.72,000 to settle his loan. Find the rate of interest per annum.

Let the rate of interest per annum be \( r\% \).

### Step 1: Calculate interest for the first 2 years
- Principal \( P_1 = 80,000 \)
- Time \( T_1 = 2 \) years

The interest for the first 2 years:
\[
I_1 = \frac{P_1 \times r \times T_1}{100} = \frac{80,000 \times r \times 2}{100} = 1,600r
\]

### Step 2: After 2 years, Raghu repaid Rs.60,000
After repaying Rs.60,000 towards the principal, the remaining principal will be:
\[
P_2 = 80,000 - 60,000 = 20,000
\]

### Step 3: Calculate interest for the next 5 years on the remaining principal
- Principal \( P_2 = 20,000 \)
- Time \( T_2 = 5 \) years

The interest for the next 5 years on \( P_2 \):
\[
I_2 = \frac{P_2 \times r \times T_2}{100} = \frac{20,000 \times r \times 5}{100} = 1,000r
\]

### Step 4: Total amount repaid after 7 years
After 7 years, Raghu repaid Rs.72,000 to settle the loan. This repayment includes the remaining principal of Rs.20,000 and the total interest accrued.

The total interest \( I \) is the sum of \( I_1 \) and \( I_2 \):
\[
I = I_1 + I_2 = 1,600r + 1,000r = 2,600r
\]

The total amount repaid is the sum of the remaining principal and the total interest:
\[
P_2 + I = 20,000 + 2,600r
\]

This total should equal the final repayment of Rs.72,000:
\[
20,000 + 2,600r = 72,000
\]

### Step 5: Solve for \( r \)
\[
2,600r = 72,000 - 20,000 = 52,000
\]
\[
r = \frac{52,000}{2,600} = 20
\]

Thus, the rate of interest per annum is \( \boxed{20\%} \).

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### Related Questions:
1. How is simple interest calculated, and how does it differ from compound interest?
2. What happens if Raghu repays the loan after 5 years instead of 7 years?
3. How would the result change if Raghu made a different partial payment after 2 years?
4. What is the formula for calculating interest when the rate is compounded annually instead of being simple?
5. How is the total repayment amount determined for loans with variable interest rates?

**Tip:** When dealing with loans and interest, always clarify whether it's simple or compound interest as they lead to different outcomes.

Learn how to calculate the rate of simple interest per annum for a loan of Rs.80,000 with repayments after 2 and 7 years. This step-by-step solution explains the use of simple interest formulas, principal repayments, and final loan settlement calculations. Suitable for Grades 9-10.

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