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How much do you need to invest today at 4% compounded semiannually if you want to have...

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spock4 | Student, Undergraduate | Honors

Posted May 26, 2012 at 7:31 PM via web

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How much do you need to invest today at 4% compounded semiannually if you want to have 5,000,000 after 2 years?

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted May 26, 2012 at 7:39 PM (Answer #1)

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An amount P invested today at a rate of interest r for n years is equal to `P(1 + r)^n` after n years.

If an amount of 5000000 is required after 2 years and the rate if interest compounded semi-annually is 4% the amount to be invested is P such that:

`P*(1 + 0.04/2)^4 = 5000000`

As the compounding is done semi-annually, the rate has been halved and the period of investment made double.

=> P = `5000000/(1.02)^4`

=> P = 4619227.13

An amount of 4619227.13 needs to be invested.

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