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GrowthRates

# GrowthRates - P(0(1 avg a nnual g ro wth ra te)^10 = P(10 A...

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How to Calculate Average Annual Growth Rates for Geometric Growth S uppo s e  P = 0.4 in Ye ar 0   and P = 0.7 in Ye ar 10 %  c hang e  fro m  Ye ar 0 to  Ye ar 10 is  (0.7 – 0.4)/0.4 = 0.75    75% Ho w to  c alc ulate  ave rag e  annual whe n g ro wth is  g e o m e tric   (c o m po unding ) Ho w abo ut 75% /10 = 7.5% ?   No t ve ry ac c urate . 0.4(1 + 0.075)^10 = 0.82. What is  ave rag e  annual?   0.4 (1 + a)^10 = 0.7.   S o lve  fo r a to  g e t a  = .058 o r 5.8% S uppo s e  P=0.4 in ye ar t=0                 =0.7 in ye ar t=10 %  c hang e  in pric e  fro m  ye ar 0 to  10 is   100 (0.7-0.4//0.4) = 75% Ho w to  c alc ulate  ave rag e  annual g ro wth whe n g ro wth is  g e o m e tric   c o m po unding . 75% /10 ye ars  = 7.5%  no t ve ry ac c urate

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Unformatted text preview: P(0) (1 +avg a nnual g ro wth ra te )^10 = P(10) A Useful Approximation S uppo s e Z = W X Y G ro wth ra te o f Z a ppro x = g ro wth ra te o f W + g ro wth ra te o f X + g ro wth ra te o f Y S uppo s e Z = X/Y. G ro wth ra te o f Z = g ro wth ra te o f X – g ro wth ra te o f Y Exa m ple : If a g g re g G DP g ro ws b y 4% pe r ye a r a nd po pula tio n g ro ws b y 1.5% pe r ye a r, wha t is g ro wth o f G DP pe r c a pita ? 4 – 1.5 = 2.5% . Z = W x Y G ro wth ra te o f Z is a ppro x g ro wth ra te o f W plus the g ro wth rate o f Y Wo rks fo r m o re tha n two additio nal g ro wth ra te s If Z = X/Y G ro wth ra te o f Z = g rwth rate o f X/ g rwth ra te o f Y...
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