the difference between the compound interest and the simple interest on a certain sum for 2years at 6% per annum is $90 .find the sum.
Answers
Answer:
there is a short trick for this q
Ans. 25,000
Step-by-step explanation:
Time should be two years
C.I-S.I=PR×R/10000 CI=Compound iterest
SI=Simple interest
P=principal
R=rate of interest for one y
90=P×6×6/10000=25,000(Ans)
Answer:
The sum is $25,000
Step-by-step explanation:
P = intial amount or principal = ?
R = rate of interest per cent per annum = 6
T = time period in years = 2
Simple Interest = SI = (P*R*T)/100
= P*6*2/100
= 12*P/100
= 0.12P
Let A be the final amount at the end of T years, based on compound interest of R per cent per year, compounded annually, with P as the intial amount. Then, we know that:
A = P*(1 + R/100)^T
Substituting, we get:
A = P*(1 + 6/100)^2
A = P*(1.06)^2
A = P*(1.1236)
Now, Compound interest (CI) = Final amount - Principal
= P*(1.1236) - P
= 1.1236P - P
= 0.1236P
We are given that difference between CI and SI is $90
=> CI - SI = 90
=> 0.1236P - 0.12P = 90
=> 0.0036P = 90
=> P = 90/0.0036
=> P = (90 * 10000)/36
=> P = (10*10000)/4 ........(9 is the cancelled common factor)
=> P = (100*1000)/4
=> P = 25*1000
=> P = 25000
The principal (intial amount) is $25,000