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maths-urgently needed

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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 - ,

    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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