In 2007, the real GDP in Northwest Island is 4 times that of Southeast Island. If real GDP in Southeast Island is growing at 10% a year, and real GDP in Northwest Island is growing at 3.5% a year, approximately how many years will it take for real GDP in the 2 islands to match? (use the rule of 70 and assume population growth is 0.) (I did not provide answers because i want to see your approach)
Lets say at time 0, SE’s GDP = x, so NE’s GDP = 4x. I know I’ll be working with rule of 70, so that means, I need something that doubles… i.e., working with the factors 2, 4, 8, 16, 32, 64, etc… So say I’m trying to aim for the “8” first, since NE’s already 4x. I want NE to double, which means from rule of 70, it’ll be 70/3.5 = 20 years. If NE doubles in 20 years, that means NE will be 8x (i.e., 8 times that of SE currently). I also know that SE doubles every 7 years (70/10 = 7 years). So after 21 years, SE will double 3 times (i.e. 2^3, which is 8). So after 20 years, NE will be 8x, and after 21 years, SE will be 8x. I guess approx 20-21 years their GDP will eventually meet. I can’t think of any other intuitive way to go about this when only using rule of 70. I feel like it’s a matter of recognizing the “2 raised to the power of” rule. Or you can just do this: Mathematically, it’s just NE = 4(SE) at time = 0 and, we have the equation => 4 (1.035)^x = (1.10)^x after x years of compounding, we have the above equation true. so solve for x, x = ln (1/4) / ln (1.035 / 1.10), giving you x = 22.76 years.
The geeky way: 4*(2^(x/20) = 2^(x/7) => 2^(2 + x/20) = 2^(x/7) => 2 + x/20 = x/7 So x = 21.5 The faster way: Just count up and realize that in 20 years NI’s GDP will be 8 and in 21 years SI’s will also be 8 (assuming starting GDP’s are 4 & 1 respectively). Therefore the answer has to be a bit more 21.
The only thing to watch out for is to NOT use the Logarithmic method as this will give you a rounded answer of 23 (while the rule of 70 gives a rounded ans of 22). And you just know CFAI will have 23 as one of the options!
I too got confused initially but was then able to get the correct answer. The mistake that I made initially was doubling the GDP of SE every 7 years based on its initial GDP.
1.065^x=4 solve for x (1.065 comes from the growth differential) x=22 years
adalfu Wrote: ------------------------------------------------------- > Lets say at time 0, SE’s GDP = x, so NE’s GDP = > 4x. > > I know I’ll be working with rule of 70, so that > means, I need something that doubles… i.e., > working with the factors 2, 4, 8, 16, 32, 64, > etc… > > So say I’m trying to aim for the “8” first, since > NE’s already 4x. I want NE to double, which means > from rule of 70, it’ll be 70/3.5 = 20 years. > > If NE doubles in 20 years, that means NE will be > 8x (i.e., 8 times that of SE currently). > > I also know that SE doubles every 7 years (70/10 = > 7 years). So after 21 years, SE will double 3 > times (i.e. 2^3, which is 8). > > So after 20 years, NE will be 8x, and after 21 > years, SE will be 8x. I guess approx 20-21 years > their GDP will eventually meet. > > I can’t think of any other intuitive way to go > about this when only using rule of 70. I feel > like it’s a matter of recognizing the “2 raised to > the power of” rule. > > > > > Or you can just do this: > > Mathematically, it’s just > > NE = 4(SE) at time = 0 > > and, we have the equation => 4 (1.035)^x = > (1.10)^x > > after x years of compounding, we have the above > equation true. > > so solve for x, x = ln (1/4) / ln (1.035 / > 1.10), giving you x = 22.76 years. why does this calculator give a different answer? http://rechneronline.de/logarithm/ i did ln4/ln1.063 and i got 22.6907
Currently: X1=4*X2 (real GDP in Northwest Island = X1 = 4 times that of Southeast Island=4*X2) In N years, the GDP of both countries would be equal: X1*(1+3.5%)^N=X2*(1+10%)^N, replace X1=4*X2 and solve for N using ln, that would be 22.76 years.
I would rather go through simple approach: First one to double its GDP 70/3.5 = 20 years ; Add few months since its actually 72 not 70. Lets say 4billion become 8. Second one in double every 7 years ( 70/10) that is 2 in seven years 4 in 14 years 8 in 21 years. Approximately 21 years is quick trial and error approach.
pacmandefense Wrote: ------------------------------------------------------- > In 2007, the real GDP in Northwest Island is 4 > times that of Southeast Island. If real GDP in > Southeast Island is growing at 10% a year, and > real GDP in Northwest Island is growing at 3.5% a > year, approximately how many years will it take > for real GDP in the 2 islands to match? (use the > rule of 70 and assume population growth is 0.) > > (I did not provide answers because i want to see > your approach) I don’t know why the rule of 70 was put in… we have a calculator… just use logs. N=northwest S=Southwest 4S=N (1.035^X)4=(1.1^X) --> Ln(1/4)/(ln(1.035/1.1)=x —> -1.38629/-.0609= 22.76
CFABLACKBELT Wrote: ------------------------------------------------------- > pacmandefense Wrote: > -------------------------------------------------- > ----- > > In 2007, the real GDP in Northwest Island is 4 > > times that of Southeast Island. If real GDP in > > Southeast Island is growing at 10% a year, and > > real GDP in Northwest Island is growing at 3.5% > a > > year, approximately how many years will it take > > for real GDP in the 2 islands to match? (use > the > > rule of 70 and assume population growth is 0.) > > > > (I did not provide answers because i want to > see > > your approach) > > > I don’t know why the rule of 70 was put in… we > have a calculator… just use logs. > > N=northwest S=Southwest > > 4S=N > > (1.035^X)4=(1.1^X) --> > > Ln(1/4)/(ln(1.035/1.1)=x —> -1.38629/-.0609= > 22.76 because what if the answer choices are: a. 20 b. 22 c. 23 you would get it wrong if you picked c. the rule of 70 estimates it to be 22 :x i bet you’ll never get this question on the exam – don’t quote me though.
adalfu Wrote: ------------------------------------------------------- > CFABLACKBELT Wrote: > -------------------------------------------------- > ----- > > pacmandefense Wrote: > > > -------------------------------------------------- > > > ----- > > > In 2007, the real GDP in Northwest Island is > 4 > > > times that of Southeast Island. If real GDP > in > > > Southeast Island is growing at 10% a year, > and > > > real GDP in Northwest Island is growing at > 3.5% > > a > > > year, approximately how many years will it > take > > > for real GDP in the 2 islands to match? (use > > the > > > rule of 70 and assume population growth is > 0.) > > > > > > (I did not provide answers because i want to > > see > > > your approach) > > > > > > I don’t know why the rule of 70 was put in… > we > > have a calculator… just use logs. > > > > N=northwest S=Southwest > > > > 4S=N > > > > (1.035^X)4=(1.1^X) --> > > > > Ln(1/4)/(ln(1.035/1.1)=x —> -1.38629/-.0609= > > 22.76 > > > because what if the answer choices are: > > a. 20 > b. 22 > c. 23 > > you would get it wrong if you picked c. the rule > of 70 estimates it to be 22 :x > > i bet you’ll never get this question on the exam > – don’t quote me though. Then you would pick 23 based on rounding… This would just be a cruel question.
(70/(10-3.5))*2=21.5385 years using the rule of 70
this is like the payback period question from L1 in june.
In 2007, the real GDP in Northwest Island is 4 times that of Southeast Island. If real GDP in Southeast Island is growing at 10% a year, and real GDP in Northwest Island is growing at 3.5% a year, approximately how many years will it take for real GDP in the 2 islands to match? (use the rule of 70 and assume population growth is 0.) if GDP of SE is x SE doubles in every 7 (7010) years while NW doubles in every 20 years so it would approximately take 20 years, when the GDP of both would be 8x, i did it today morning, remember vividly
here are the answer choices A) 40.0 years. B) 24.5 years. C) 14.0 years. the official explanation Southeast Island is doubling every 7 years. Northwest Island is doubling every 20 years. The correct calculation is = 70 / (r1 / r2) = 70 / (10 / 3.5) = 70 / 2.857 = 24.5 how do they determine which rate is r1 from r2, if u assume r2 is 10 and r1 is 3.5, the answer is obviously gonna be diff
pacmandefense Wrote: ------------------------------------------------------- > adalfu Wrote: > -------------------------------------------------- > ----- > > Lets say at time 0, SE’s GDP = x, so NE’s GDP = > > 4x. > > > > I know I’ll be working with rule of 70, so that > > means, I need something that doubles… i.e., > > working with the factors 2, 4, 8, 16, 32, 64, > > etc… > > > > So say I’m trying to aim for the “8” first, > since > > NE’s already 4x. I want NE to double, which > means > > from rule of 70, it’ll be 70/3.5 = 20 years. > > > > If NE doubles in 20 years, that means NE will > be > > 8x (i.e., 8 times that of SE currently). > > > > I also know that SE doubles every 7 years (70/10 > = > > 7 years). So after 21 years, SE will double 3 > > times (i.e. 2^3, which is 8). > > > > So after 20 years, NE will be 8x, and after 21 > > years, SE will be 8x. I guess approx 20-21 > years > > their GDP will eventually meet. > > > > I can’t think of any other intuitive way to go > > about this when only using rule of 70. I feel > > like it’s a matter of recognizing the “2 raised > to > > the power of” rule. > > > > > > > > > > Or you can just do this: > > > > Mathematically, it’s just > > > > NE = 4(SE) at time = 0 > > > > and, we have the equation => 4 (1.035)^x = > > (1.10)^x > > > > after x years of compounding, we have the above > > equation true. > > > > so solve for x, x = ln (1/4) / ln (1.035 / > > 1.10), giving you x = 22.76 years. > > why does this calculator give a different answer? > http://rechneronline.de/logarithm/ > > i did ln4/ln1.063 and i got 22.6907 nevermind. rounding errors