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26 September, 04:41

An investment that you are considering promises to pay $2000 semiannually for the next two years, beginning six months from now. You have determined that the appropriate opportunity cost (discount rate is 8%, compounded quarterly. What is the value of this investment?

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  1. 26 September, 05:44
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    The present value is = $7325.48

    Explanation:

    Step 1: Know the formula for the Present Value of the investment

    PV formula = PMT x [1 - (1 / (1 + r) ^n) ] / r

    Where PMT = Annuity Amount

    r = Discount Rate

    n = number of years or period

    Step 2: fill in the necessary figures for the formula

    PMT = $2000

    Semi-annually = 2000/2 = 1000

    r = 8%, however, compounded quarterly = 8/4 (quarter) = 2% per quarter

    n = 2 years ... however since it is to be compounded quarterly, 2 x 4 (quarterly compounding) = 8

    Therefore, Present Value =

    The semi - annual PMT, the 2% quarterly rate, the 8 for number of years will be used

    PV = 1000 x [1 - (1 / (1 + 0.02) ^8] / 0.02

    = 1000 x 7.32548

    The present value of the investment is = $7325.48
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