Question

The difference between the compound interest and simple interest on ₹ 7500 for 2 years is ₹ 27 at the same rate of interest per year. Find the rate of interest.

Answer 1

Given:

• Principal (P = ₹ 7500)
• Time (T = 2) years
• Difference between compound interest (C.I.) and simple interest (S.I. = ₹ 27)
• Rate of interest (R%) per annum to be found

Step-wise calculation:

1. Simple Interest (SI) formula: 

`S.I. = (P xx R xx T)/100`

`S.I. = (7500 xx R xx 2)/100`

S.I. = 150R

2. Compound Interest (CI) for 2 years: 

Amount `A = P(1 + R/100)^2`

Compound interest: 

C.I. = A – P

`C.I. = 7500(1 + R/100)^2 - 7500`

3. Difference between CI and SI:

C.I. – S.I. = 27

Substitute (C.I.) and (S.I.): 

`7500(1 + R/100)^2 - 7500 - 150R = 27`

4. Simplify: 

`7500((1 + R/100)^2 - 1) = 27 + 150R`

Expand square:

`(1 + R/100)^2 = 1 + 2 R/100 + (R/100)^2`

`(1 + R/100)^2 = 1 + (2R)/100 + R^2/10000`

So, `7500((2R)/100 + R^2/10000) = 27 + 150R`.

5. Multiply terms:

`7500 xx (2R)/100 = 150R`,

`7500 xx R^2/10000 = (7500R^2)/10000`

`7500 xx R^2/10000 = 0.75R^2`

So, 150R + 0.75R² = 27 + 150R.

6. Subtract 150R from both sides:

0.75R² = 27

7. Solve for R²:

`R^2 = 27/0.75`

R² = 36

Therefore, `R = sqrt(36) = 6`.