Posted by **Anonymous** on Monday, January 21, 2013 at 6:31am.

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?

- maths-urgently needed -
**Reiny**, Monday, January 21, 2013 at 10:30am
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!

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