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Present Value Problem from Broverman's Text (Will you check my solutio

  1. May 13, 2013 #1
    1. The problem statement, all variables and given/known data

    Hello all, I am doing problem 2.1.15 from "The Mathematics of Investment and Credit" 5th ed.

    I'm having trouble with the PV solution...I think I may be counting my days wrong.

    Here is the original problem:
    Since June 30, 2007 Smith has been making deposits of 100 each into a bank account on the last day of each month. For all of 2007 and 2008 Smith's account earned nominal interest compounded monthly at an annual rate of 9%. For the first 9 months of 2009 the account earned i(12) = 9%. For the first 9 months of 2009 the account earned i(12) = .105, and since then the account has been earning i(12) = .12.

    Find the PV on June 1, 2007 of all payments made in 2007, 2008, 2009.


    3. The attempt at a solution
    Now in my solution I broke it in to 3 parts (each for each interest rate).

    2008 - 2009: i-effective = .09/12 = .0075
    PV = 100*[((1-(1/1.0075)^19)/.0075)] = 1764.68
    (19 months worth of payments).

    (3/4) 2009: i-effective = .105/12 = .00875
    PV = 100*[((1-(1/1.00875)^9)/.00875)]*[(1/1.0075)^19] = 747.79
    (9 months worth of payments multiplied by the 19 months rate)

    (1/4) 2009:
    PV = 100*[((1-(1/1.01)^3)/.01)]*[(1/1.0075)^19]*[(1/1.00875)^9] = 235.93
    (3 months worth of payments (including last) multiplied by the 19 and 9 months rates)

    Last payment on Dec 31, 2009:
    PV = 100*[(1/1.0075)^19]*[(1/1.00875)^9]*[(1/.01)^3] = 77.86

    However, summing these up I get 2826.26 though the solution gets 2825.49.

    I know it is very close, but I want to be assured that my solution is not in error. Thank you!
     
  2. jcsd
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