Question

A sum of Rs. 7500 amounts to Rs. 9075 at 10% p.a, interest being compounded yearly in a certain time. The simple interest (in Rs.) on the same sum for the same time and the same rate is:
1. 1500
2. 1530
3. 1480
4. 1520

Answer 1

Correct Answer - Option 1 : 1500

Given:

A = 9075

P = 7500

R = 10%

Formula used:

A = P(1 + r/100)ⁿ

SI = (P × R × T)/100

where,

A = Amount

P = Principal

r = Rate of Interest

n = number of years

SI = Simple Interest

Calculation:

A = P (1 + r/100)ⁿ

⇒ 9075 = 7500( 1 + 10/100)^T

⇒ 9075/7500 = (1 + 1/10)^T

⇒ 121/100 = (11/10)^T

⇒ (11/10)² = (11/10)^T

⇒T = 2 years

Now, 

P = 7500

R = 10%

T = 2 years

SI = P × R × T/100

⇒ (7500 × 10 × 2)/100

⇒ 1500

∴ The simple interest is 1500