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Suppose that P dollars is invested in a savings account at interest rate I, compounded semiannually, for one year. The amount A in the account after one year is given by A = P(1 + i/2)^2

I got help with a problem similar to this earlier, but I still do not understand.

Thank you! :-)

  • Algebra -

    interest rate is i per year
    so it is i/2 for half a year
    every half hear you multiply by (1+i/2)
    so after 1 year, two half years, you multiply by (1+/2)(1+i/2) = (1+i/2)^2

    say i = 20% = .20
    that is 10% per half year or .10 added every half year
    so after a half year we have P + .10 P = P(1.10)
    after a whole year, multiply by (1.1 again
    P (1.10)^2 = 1.21 P

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