Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Something grows at an annualized rate of 5% for 4 months and then declines at an annualized rate of 4% for the next four months. What would be the annualized growth rate over the entire 8 month period?

I am conflicted if I should use a geometric mean of 5% an -4% or if I should do (1+0.05)(1-0.04)-1 = 0.8%. Thanks for the help

share|improve this question

1 Answer 1

up vote 1 down vote accepted

If it grows at an annualized $5\%$ for $4$ months it grows by $\frac{5}{3}\%$ (or a bit more if you compound), then falling at $4\%$ for $4$ months it falls by $\frac{4}{3}\%$. Your last is correct if you get the correct growth rates: $(1+\frac{5}{3}\%)(1-\frac{4}{3}\%)-1$, which I make growing by $\frac{7}{2250}$ or about $0.31111\%$ in $8$ months. To annualize this, we should mutiply by $\frac{3}{2},$ getting $\frac{21}{4500}\approx 0.46667\%$

share|improve this answer
    
Is 0.31111% annualized? –  icobes Oct 1 '11 at 23:01
    
@icobes: No, it is the amount of growth. I'll fix it. –  Ross Millikan Oct 1 '11 at 23:17

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.