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
Answers
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)