Question

On what sum of money will the difference between compound and simple interest for 2 years at 6% per annum be equal to ₹ 72?

Answer 1

Given:

We need to find the sum of money (Principal P) such that the difference between the compound interest (C.I.) and simple interest (S.I.) for 2 years at 6% per annum is ₹ 72.

Step-wise calculation:

1. Let the principal be P, rate of interest (r = 6%) and time (n = 2) years.

2. Simple Interest (S.I.) for 2 years:

`S.I. = (P xx r xx n)/100`

`S.I. = (P xx 6 xx 2)/100`

`S.I. = (12P)/100`

S.I. = 0.12P

3. Compound Interest (C.I.) for 2 years: 

`A = P(1 + r/100)^n`

`A = P(1 + 6/100)^2`

A = P(1.06)²

A = P × 1.1236

C.I. = A – P

C.I. = P × 1.1236 – P

C.I. = P × (1.1236 – 1)

C.I. = 0.1236P

4. Difference between C.I. and S.I.: 

C.I. – S.I.

= 0.1236P – 0.12P

= 0.0036P

5. Given that this difference is ₹ 72: 

0.0036P = 72

6. Solve for P:

`P = 72/0.0036`

P = 20000

The sum of money on which the difference between compound interest and simple interest for 2 years at 6% per annum is ₹ 72 is ₹ 20,000.