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First I need a sanity check for my calculations.

Say I have this scenario:

Nominal Rate (per year) [r] 13%
Inflation Rate (per year) [i] 5%
Initial investment [x] $ 100.00
Time (years) [t] 10
Tax [T] 15%

I want to calculate the real rate (Y) of this investment.

First I need to get the gross value (G):

G = x * (1 + r)t = 100.00 * (1 + 13%)10 = $ 339.46

Then the I get the net value after taxation (N)

N = G - (G - x) * T = 339.46 - (339.46 - 100.00) * 15% = $ 303.54

Then I bring this to present value with the inflation rate, which will be the real value (R):

R = N * (1 + i)-t = 303.54 * (1 + 5%)-10 = $ 186.35

To get the real rate (Y) I need to use the rate formula:

Y = (R / x)1/t - 1 = (186.35 / 100.00)1/10 - 1 = 6,42%

So in this investment my money really grows 6,42% per year. Is that right? Is there a better way to calculate this? this seems very laborious.

In Excel I'm using this monstrosity:

=rate(10;;-100;-pv(5%;10;;fv(13%;10;;-100)-(fv(13%;10;;-100)-100)*15%))
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  • I never understood the point of calculating a “real” rate of return controlling for things that any alternative investment would also be subject to. What matters is, does this investment appropriately compensate for risk compared to other investment alternatives.
    – quid
    May 22 at 16:34
  • Well, with that you can make other predictions, say if the infation rate goes up, how bad it will affect my investment, what's the threshold for real return? But yeah, it's hard to use to get 'real' values because it will definitly deviate May 22 at 16:43
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You can get an estimate of the real rate of return after taxes by using:

(13% - 5%) * (1-15%) = 8% * 85% = 6.8%

or just take out the intermediate parts that cancel out:

((((1+13%)^10-1)*85%+1)^(1/10)/(1+5%) -1 = 6.42%
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