Question

8. If the difference between compound
interest and simple interest on a
certain sum of money for 2 years at 9%
per annum is 21.87 the sum is.​

Answer 1

Answer:

The initial amount is Rs.2700

Step-by-step explanation:

P = initial amount

R = rate of interest per cent per year  = 9

T = time period in years  = 2

A = final amount at the end of T years

Simple Interest:

SI = (P*R*T)/100

SI = (P*9*2)/100

SI = (18*P)/100

SI = 0.18*P

Compound interest

A = P(1 + R/100)^T

A = P(1 + 9/100)^2

A = P(1 + 0.09)^2

A = 1.1881*P

CI = A - P

    = 1.1881*P - P

     = 0.1881*P

Difference between CI and SI is given to be 21.87

=> 0.1881*P - 0.18*P = 21.87

=> 0.0081*P = 21.87

=> P = 21.87/0.0081

=> P = 218700/81        

=> P = 2700

The initial amount (sum) is Rs.2700