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

[Hodgey8806]

Homework Statement

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.

The Attempt at a Solution

Now in my solution I broke it into 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!

 

[lippyka]

</code>Homework Equations PV = PMT*[((1-(1/1+i)^n) / i)]PMT = 100The Attempt at a SolutionIt looks like you did the calculations correctly. The discrepancy is most likely due to rounding errors. Your calculation of 2826.26 is correct, and the solution's result of 2825.49 is also correct.