I'm working on the following problem at the moment while preparing for an exam.
Find the present value of payments of 200 every six months starting immediately and continuing through four years from the present, and 100 every six months thereafter through ten years from the present, if i^(2) = .06. (all quantities in dollars)
Since interest is given, and not discount I went ahead and calculated this as an annuity immediate instead of an annuity due.
$\displaystyle a=\frac{1-v^n}{i}=\frac{1-1.03^{-9}}{.03}= 7.786108922$
$\displaystyle a\times200=1557.221784$
So far so good. Here's where I think I might be doing something wrong. For the last six years of the annuity, I'm calculating the present value four years in the future and then discounting that another four years. Is this wrong?
$\displaystyle 100a= 100\times\frac{1-1.03^{-18}}{.03}=1063.495533$
So this is the present value of the last six years of the annuity at time four into the future. I discount it four years to get:
$\displaystyle 1063.495533\times\nu^8=839.5331944$
To answer the question, I get 2,396.75. The book gives 2,389.72, which is quite close. Can anyone account for the difference?