if the simple interest on a sum of money at 5% per annum for 3 yr is rupees 1200, the compound interest for the same sum for the same period at the same rate is
Answers
Answer:
Rs.1261
Step-by-step explanation:
P = initial amount
R = rate of interest per cent per year = 5
T = time period in years = 3
SI = simple interest = (P*R*T/100)
Now,
SI = 1200 ...(given)
=> (P*R*T)/100 = 1200
=> (P*5*3)/100 = 1200
=> 15P = 120000
=> P = 120000/15
=> P = 8000
The initial amount (or principal) is Rs.8000
Now,
According to compound interest formula
A = amount at the end of time period T is given by P(1 + R/100)^T
We are given that sum, period and rate of interest is the same
=> P= 8000; R = 5; T = 3
Using the values of P, R and T, we get
A = 8000*(1 + 5/100)^3
A = 8000*(1.05)^3
A = 8000*1.157625
A = 9261
Compound interest = CI = A - P
CI = 9261 - 8000
CI = 1261
The required compound interest = Rs.1261
compound intrest = Rs.1261
Step-by-step explanation:
Given:-
Rate of intrest (R) = 5%
Time (T) = 3 year's
Intrest (I) = 1200
Principle (P) = ??
we know that
I = PTR/100
substitute known values above identity
1200 = [ P × 3 × 5 ] /100
P = ( 1200 × 100 ) /5 × 3
P = 8000
Now according to question to find CI
we know that
CI = P[ (1 + R/100)^n -1 ]
here
CI = compound intrest
P = principle amount [ 8000 ]
R = Rate of intrest [ 5% ]
n = Time [ 3 year's ]
CI = 8000 [ (1 + 5/100)^3 - 1 ]
CI = 8000 [ 1+1/20)^3- 1 ]
CI = 8000 [ {(20 + 1)/20}^3 - 1 ]
CI = 8000 [ (21/20)^3 - 1 ]
CI = 8000 [ 9261/8000 - 1 ]
CI = 8000 [ (9261 - 8000)/8000 ]
CI = 8000 × 1261/8000
CI = 1261.