For an example, have p=.4 for an interest rate of .1 and $p = .6$ for an interest rate of $-.05$, It seems to me that the average interest rate should be $.1(.6) -.05(.6) = .01$, but when I plug the numbers into excel with $100$ data points I get an average interst rate of about .00737. What am I doing wrong?
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I get $1%$ as well. I dont know what went wrong by using excel. – callculus42 Sep 11 '20 at 19:39
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Presumably $.1(.4)$ ? – Sep 11 '20 at 19:41
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Compound interests are not additive.
$$p_1(1+r_1)^n+p_2(1+r_2)^n\ne(1+p_1r_1+p_2r_2)^n.$$
The equivalent rate after $n$ periods would be
$$\sqrt[n]{p_1(1+r_1)^n+p_2(1+r_2)^n}-1.$$
It is not constant, as it depends on $n$.
With simple interests the weighted average works:
$$p_1(1+nr_1)+p_2(1+nr_2)=1+n(p_1r_1+p_2r_2).$$