Certainly! Let's solve this problem step-by-step.
### Step 1: Calculate the Simple Interest for Sheela
Sheela borrows ₹15000 at an interest rate of 12% per annum for 3 years using simple interest.
The formula for simple interest (SI) is:
[tex]\[ \text{SI} = \text{Principal} \times \text{Rate} \times \text{Time} \][/tex]
Where:
- Principal [tex]\( P = ₹15000 \)[/tex]
- Rate [tex]\( R = 12\% = 0.12 \)[/tex] per annum
- Time [tex]\( T = 3 \)[/tex] years
Plugging in these values:
[tex]\[ \text{SI} = 15000 \times 0.12 \times 3 \][/tex]
[tex]\[ \text{SI} = 5400 \][/tex]
So, Sheela pays ₹5400 as simple interest over 3 years.
### Step 2: Calculate the Compound Interest for Renu
Renu borrows ₹15000 at an interest rate of [tex]\( 10 \frac{1}{2}\% \)[/tex] per annum, which is compounded annually for 3 years.
The formula for compound interest (CI) is:
[tex]\[ \text{A} = \text{Principal} \times (1 + \text{Rate})^\text{Time} \][/tex]
[tex]\[ \text{CI} = \text{A} - \text{Principal} \][/tex]
Where:
- Principal [tex]\( P = ₹15000 \)[/tex]
- Rate [tex]\( R = 10.5\% = 0.105 \)[/tex] per annum
- Time [tex]\( T = 3 \)[/tex] years
Plugging in these values:
[tex]\[ \text{A} = 15000 \times (1 + 0.105)^3 \][/tex]
[tex]\[ \text{A} = 15000 \times (1.105)^3 \][/tex]
[tex]\[ \text{A} \approx 15000 \times 1.348855125 \][/tex]
[tex]\[ \text{A} \approx 20238.489375 \][/tex]
Now, calculate the compound interest:
[tex]\[ \text{CI} = \text{A} - \text{Principal} \][/tex]
[tex]\[ \text{CI} = 20238.489375 - 15000 \][/tex]
[tex]\[ \text{CI} \approx 5238.489375 \][/tex]
So, Renu pays approximately ₹5238.49 as compound interest over 3 years.
### Step 3: Calculate the Difference in Interest Paid
Now, we compare the interest paid by Sheela and Renu to determine who pays more and by how much.
Sheela's interest: ₹5400.00
Renu's interest: ₹5238.49
The difference in interest paid is:
[tex]\[ \text{Difference} = \text{Sheela's Interest} - \text{Renu's Interest} \][/tex]
[tex]\[ \text{Difference} = 5400.00 - 5238.49 \][/tex]
[tex]\[ \text{Difference} \approx 161.51 \][/tex]
So, Sheela pays ₹5400.00 while Renu pays approximately ₹5238.49. The difference is approximately ₹161.51.
### Conclusion
Sheela pays more interest than Renu. The amount by which Sheela's interest exceeds Renu's is ₹161.51.
