Question

On what sum of money does the does the difference between the simple interest and compound interset in 2 years at 5 percent per annum is rs.15

Answer 1

Answer:

The required sum of money (principal) is Rs.6000

Step-by-step explanation:

We are given:

P = ?

R = rate of interest per cent per year = 5

T = number of years = 2

Now:

Simple interest = SI = (P*R*T)/100

SI = (P*5*2)/100

    = 10*P/100

     = 0.1*P

Compound interest = CI = A - P

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

Substituting, we get:

A = P(1 + 5/100)^2

   = P(1.05)^2

   = 1.1025*P

=> CI = 1.1025*P - P

         = 0.1025*P

We are given that difference between CI and SI is Rs.15

=> 0.1025*P - 0.1*P = 15

=> 0.0025*P = 15

=> P = 15/0.0025

=> P = 6000

The required principal is Rs.6000

Verify:

P = 6000; R = 5; T = 2

SI = (6000*5*2)/100 = 600

A = 6000*(1 + 5/100)^2

   = 6000*(1.05)^2

   = 6000*(1.1025)

   = 6615

CI = A - P = 6615 - 6000 = 615

CI - SI = 615 - 600 = 15 .......(Difference of Rs.15 verified)