A sum of ₹10,000 is borrowed at a rate of interest 15% per annum for 2 years. Find the simple interest on this sum and the amount to be paid at the end of 2 years.

Steps to Solve

1. Identify the formula for Simple Interest

The formula for calculating simple interest (SI) is given by:

$$ SI = \frac{P \times R \times T}{100} $$

where:
$P$ = Principal amount (the initial sum of money)
$R$ = Rate of interest per annum
$T$ = Time in years

2. Substitute the values into the formula

In this case:
$P = 10000$ (the borrowed sum)
$R = 15$ (interest rate)
$T = 2$ (time in years)

Substituting these values into the formula gives:

$$ SI = \frac{10000 \times 15 \times 2}{100} $$

3. Calculate the Simple Interest

Now, calculate the simple interest:

$$ SI = \frac{300000}{100} = 3000 $$

So, the simple interest for 2 years is ₹3000.

4. Calculate the total amount to be paid back

The total amount (A) to be paid back at the end of 2 years is the sum of the principal amount and the simple interest:

$$ A = P + SI $$

Substituting in the values gives:

$$ A = 10000 + 3000 $$

5. Final Calculation for Total Amount

Thus, the total amount to be paid back is:

$$ A = 13000 $$