Question
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?
the compound interest for the same amount for the same period is 410.
find the principal and rate of interest?
Answers
Reiny
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
<b> 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!</b>
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
<b> 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!</b>