This question is directed to the number tinkerers on the forum. I'm trying to understand a calculation on the Bogleheads Wiki and I'm totally mystified. On the I-bonds page, under "Caveats", there is a sample calculation that goes like this:
I don't get it, can someone explain how this calculation works? What are all the factors and terms? I understand the tax factor, (1-0.35), and I think the factor of 1/(1.03^30) accounts for inflation, but I don't get why that works.here is the after-tax, after-inflation value of $1 invested I bonds compounded for 30 years with 3% inflation and 1% fixed rate and then redeemed in the 35% federal income tax bracket:
(1+(1.04015^30-1)*(1-0.35)) / (1.03^30) = $1.0165153416
Here's how I would do the calculation, and I assume that I'm the one who's wrong:
P(t) = Po[1+(r-i)/n]^nt * (1-0.35)
P(t) = value of your money at year t
Po = P(0) = your initial investment value
r = composite rate = fixed rate + 2 x semiannual inflation rate + fixed rate x semiannual rate
i = annual inflation rate over period of investment, assumed to be a fixed parameter
n = number of compounding cycles per year = 12 for I-bonds
Also, I assume inflation compounds negatively with the same frequency that interest compounds positively.
According to me, the answer should be P(30) = 2.17318, with Po = 1, r = 0.0703 = .01 + 2*.03 + .01*.03, i = .03. So after 30 years you ought to have $2.17 real. Where have I screwed up?
Many thanks. Also: if you can suggest some books to help me familiarize myself with important personal finance calculations, I'd appreciate it. I am a scientist by training and I won't settle for a book that states formulae without providing derivations or proofs.