Given:
Simple interest = Rs. 540
Time = 3 years
Compound interest = Rs. 376.20
Time of compound interest = 2 years
Formula Used:
When calculated at simple interest
Interest = (p × r × t) / 100
Where p, r and t respectively are principal, rate of interest and time
When calculate at compound interest
Amount (A) = p (1 + r / 100)n
Where p, r and n respectively are principal, rate of interest and time
Calculation:
Let principal be x and rate of interest be r%
540 = (x × r × 3) / 100
⇒ r = 18000 / x
Then simple interest for 3 years, at the rate n%, = x × n × 3 / 100 = 540
Simple interest for one year = 180
Simple interest for two years = 360
Compound interest for two years = x(1 + n / 100)2 - x = 376.20
Hence the additional interest for the second year = 376.20 - 360 = 16.20
Hence the rate of interest = 16.20 / 180 × 100 = 9
∴ The principal amount = 180 / 9 × 100 = 2000