the simple interest of certain amount for a period of 2 years is 400 .
the compound interest for the same amount for the same period is 410.
find the principal and rate of interest?
let the principal be P
let the rate be i
simple interest:
I = PiT
400 = 2Pi
Pi = 200 --- P = 200/i
compound interest
P(1+i)^2 - P = 410
P( (1+i)^2 - 1) = 410
P = 410/(1 + 2i + i^2 - 1)
= 410/(i^2 + 2i)
410/(i^2 + 2i) = 200/i
200i^2 + 400i = 410i
200i^2 - 10i=0
i(200i-10) = 0
i = 0 or i = 10/200 = .05
if i = .05 , then P = 200/.05 = 4000>/b>
( I rejected i = 0 , since it would make P as undefined)
check:
simple interest
I = prt = 4000(.05)(2) = 400
compound interest
Amount = 4000(1.05)^2 = 4410
interest = 4410-4000= 410 , looks good!