Question

On what sum of money will the difference between compound and simple interest for 2 years at 5% per annum be equal to ₹ 30?

Answer 1

Given problem:

Find the sum of money (P) on which the difference between the compound interest (C.I.) and simple interest (S.I.) for 2 years at 5% per annum is ₹ 30.

Step 1: Write down the formula for the difference between compound interest and simple interest for 2 years.

The difference between C.I. and S.I. for 2 years at rate (R%) is given by:

Difference = `P xx (1 + R/100)^2 - P - (P xx 2 xx R/100)`

Simplifying:

= `P[(1 + R/100)^2 - 1 - (2R)/100]`

Expanding `(1 + R/100)^2`:

= `P[1 + 2 xx R/100 + (R/100)^2 - 1 - (2R)/100]`

= `P xx (R/100)^2`

Hence, the difference = `P xx (R/100)^2`.

Step 2: Substitute given values

Given:

R = 5%

Difference = ₹ 30 

Using the formula:

`30 = P xx (5/100)^2`

`30 = P xx 25/10000`

`30 = (25P)/10000`

Step 3: Solve for P

`30 = (25P)/10000`

Multiply both sides by 10000:

300000 = 25P

Divide both sides by 25:

`P = 300000/25`

P = 12000

The sum of money on which the difference between compound interest and simple interest for 2 years at 5% per annum is ₹ 30 is ₹ 12,000.