OvermindDL1 Report post Posted March 24, 2003 I have Math class in about an hour and need help on two last problems (I knew I shouldn't have spent so much time after High School before going to Collage, word of advice, GO AS SOON AS YOU GET OUT!!!), and I am not good at Word Problems... 1) How long does it take for a deposit of $1000 to double at 8% compounded continuously? 2)Ben Franklin's gift of $4000 to Philadelphia grew to $2 million in 200 years. At what interest rate compounded monthly would this growth occur? (I really hate word problems, I can do the real work just fine, in my head, but not these) Share this post Link to post Share on other sites

Guest Report post Posted March 24, 2003 First, there are plenty of places to look up the information to solve both of these problems such as this Professor at FSU's page. Anyway, I won't give you the answer, but I will show you how to reach it(which is for all intents and purposes giving you the answer). Now the equation for continuous compounding is FV = P*e^((periods)*(interest rate)) FV : Future Value P = Principal(ie how much money you start with) e : natural logarithm so you need to find the time it takes to double 2*P = P*e^((x)*(interest rate)) cancel out the P's so 2 = e^((x)*(interest rate)) take the natural logarithm ln 2 = x*interest rate and divide by the interest rate so (ln 2)/(interest rate) = time necessary to double As for number 2, it just uses the base FV=PV(1+i)^n or Future Value = Present Value*(1+interest rate)^(number of compound periods) so for this you know PV, FV, and n, so you just need to reform the equation to solve for i. FV/PV = (1+i)^n (FV/PV)^(1/n) - 1 = i Now all you need to do is plug and chug and you'll have the answer. With word problems it is often best to write down what you know, the necessary equations in order to solve for it and go from there. Anyway, good luck. Share this post Link to post Share on other sites

Tyrn Report post Posted March 24, 2003 quote:Originally posted by Overmind: I have Math class in about an hour and need help on two last problems (I knew I shouldn't have spent so much time after High School before going to Collage, word of advice, GO AS SOON AS YOU GET OUT!!!), and I am not good at Word Problems... 1) How long does it take for a deposit of $1000 to double at 8% compounded continuously?The formula for continuous compounding is FV = Pe^{Yr} where FV is Future Value. P is your principle, Y is the number of years and r is the rate. Your question is this: 2P = Pe^{Yr} Your principle is the amount of money you deposit. Your rate is your interest rate and e is the constant e. Plug your values in and solve for Y. quote: 2)Ben Franklin's gift of $4000 to Philadelphia grew to $2 million in 200 years. At what interest rate compounded monthly would this growth occur? The formula for periodic compounding is FV = P(1 + r/n)^{Yn} The values come from the same location as the other problem. You know what the future value, principle and time are. This time you need to solve for r (btw n=12). Share this post Link to post Share on other sites

Charles Lindsey Report post Posted March 24, 2003 That was neat. I love the internet. I used to be good at math. http://www.fool.com/fribble/2001/fribble010718.htm I like the way this formula is written better. --------------------- From article------------ The formula simply states that the amount of money you will realize from a compounding investment (otherwise known as the Future Value or "FV") is equal to the number 1 plus your periodic interest rate raised to the number of time periods you invest the money. For example, if you put $1,000 into a bond at 8% interest rate for 30 years, then the amount of money you would receive would be $1,000 times 1.08 to the 30th power. Mathematically, it looks like this: FV = $1,000 * (1 + .08) ^30 -------------- The article goes on and explains how to calculate for periodic additions of money. I have forgotten (if I ever knew) how to sovle for powers. I think Friez12 explained it well. Share this post Link to post Share on other sites

OvermindDL1 Report post Posted March 24, 2003 Thank very much for helping, I can do the normal problems givin out to me but when it comes to word problems for some reason I just skip em by, I can do those calculations in my head so they are easy enough, I just don't like word problems, had a bad experience in elementary... Again thank you... Share this post Link to post Share on other sites

Charles Lindsey Report post Posted March 24, 2003 My dad can do math in his head. Drives me crazy because sadly I did not inherit that ability. I can do it in the air though. I used to amuse myself on long trips by calculating the speed of the vehicle by using a watch to time mile markers then algebra to solve for the mph. The bad thing about word problems is they are so stupid. You look at them and sometimes wonder what they were smoking when they thought them up. The absolutely terrible thing about word problems is that they everywhere in real life. How much more will you bring home after that 3% raise? Out of that 3% they keep 1.5% for insurance. Then you have to figure taxes and withholdings. Ughh. It's gonna get extra cold and your antifreeze isn't stout enough. How much of your 30% mixture do you drain from your 4 gal system to add pure antifreeze resulting in a proper 50% mixture? Consider word problems as what you would ask yourself if you were in that situation. They are rough but they do help you out later in life. Share this post Link to post Share on other sites

OvermindDL1 Report post Posted March 25, 2003 I agree, funny thing those were the only 2 word problems, only because they were required. My Math110 teacher hates word problems too and keeps them to a minimum. I passed my test with flying colors today because it did not have word problems thankfully. First one done, took me 13 min., took the next person a little over 45 min., do not quite see how. I barely even used my graphing calculator. Something that is really sad (and this is completely a true story) is that back in high school in one of my classes, on the first day of class my teacher put some simple equations on the board and said to solve them in our head and write down our answers on a sheet of paper then put your hand up. The first set was 4 equations each having 4 sets of 4 numbers (ex. 3865+3729+9682+4729=X), I was the first one up and when every one was done (which took too long of a time) she then said the answers and for everyone who had them all right to keep their hand up, out of a class of 29, only 4 had them all correct, I was one. Next she had us do it again but with subtraction (ex. 8490-285-392-694=X) , 4 sets of those kind of equations. I was the only one in the class with them all correct. Now what I am getting at is, can I join any of you? The absolute stupidity in this area might be contagious and I really need to get out of here, anyone here live near a good IT collage like Texas Tech or Westwood or something and wouldn't mind a room-mate? EDIT: Sorry if I seem a little hot but I just got out of CIS 120 (Microsoft Office, mastered about a decade ago) and my teacher likes everything on paper, I complete 4 weeks worth of assignments that day in class and I did todays test in that class in 10 min. when it took everyone else about an hour and a half. Needless to say because my margins were off by a quarter of an inch on the excel work it got trashed. It was perfect in every way except for the printer I printed off of, I didn't even turn in any work on paper in my English class, teacher wanted everything through email or CD or something other then paper. The only thing I like on paper are game manuals or something else relating. I actually judge a game very highly on its manual, I practically memorize the manual before I go ingame. The BCM manual is, for example, extremely well done, much better then many others. I like manuals like the one that came with SC3000 Unlimited and such, I may never play that game but I still love to read the manual, hundreds of pages thick. [ 03-24-2003, 09:44 PM: Message edited by: Overmind ] Share this post Link to post Share on other sites

Rico Jansen Report post Posted March 25, 2003 I don't think that formula with the natural logarithem is the the right one. I agree with Chavik. Assuming it's a one-time deposit of $1000. FV=PV*(1+interest)^years In the case of the first problem where you need to figure out the number of years: 1: divide both sides by PV: FV/PV=(1+interest)^years 2: to calculate the exponent (years) one takes the logarithm (of any base;i.e. 10 or e) on both sides of the equation; and taking the logarithm of (base^exponent) is equal to exponent*logarithm of (base) So: 10log (FV/PV)= 10log( (1+interest)^years ) which is: 10log(FV/PV) = years* 10log(1+interest) 3: The number of years is now the division of the to 10log's years= 10log(FV/PV) / 10log(1+interest) 4: Inserting the numbers: FV/PV=2000/1000=2; 1+interest=1+0.08=1.08 Ending up with: years= 10log(2) / 10log(1.08) The answer is.... (drum noise) .... quite close to! .... count all your fingers and forget one. The answer is not the same as the formulas from Friez or Tyrn suggests. It's not far off perhaps. But not it. As for the second problem they're both right. In a way, that is. Friez's formula works if i is the interest per month, while Tyrn expects r (rate??) to be an anual interest (per year) as he divides r by the number of months. Hope this is not too late for class. Good luck. Share this post Link to post Share on other sites

OvermindDL1 Report post Posted March 25, 2003 Its only late by about 6 hours (insert smiley with tounge if I used them, I only insert them in extremely rare and very useful occasions)... plus I figured it out by combining the previous formulas..., thanks though. Share this post Link to post Share on other sites

Tyrn Report post Posted March 25, 2003 quote:Originally posted by Rico Jansen: The answer is not the same as the formulas from Friez or Tyrn suggests. It's not far off perhaps. But not it. Personally, I hate accounting math...it's black magic if you ask me. http://www.moneychimp.com/articles/finwork...compounding.htm http://cs.selu.edu/~rbyrd/math/continuous/ http://www.math2.org/math/general/interest.htm <- easiest to read http://www.math.sc.edu/~leschins/Math122HW...uous_growth.htm Share this post Link to post Share on other sites

Charles Lindsey Report post Posted March 25, 2003 Aww hell. Let's talk math for a bit. I'm tired of solving the world's problems anyway. The antifreeze question was a real problem I had in seventh grade. Once again I do not remember the answer or the procedure to calculate the answer. I guesstimate and I get real darn close. If that's doing math in my head it's on such a subconscious level I'm not aware of it. The "funny" (strange) thing about the antifreeze problem is that while it may be technically and mathematically correct it just don't work that way. Engines tend to form pockets of "vacuum" and you can never drain all that antifreeze. Just for fun: Derek threw out some figures and I calculated the diameter of Galcom. I bought a new tractor. Well... riding lawn mower. It has a 42" cut. My old one has a 38" cut. My father was calculating 10 passes = 420" vs 380". Screw that. I went for the fuzzy math. The new tractor has a 4" greater cut than the old one. 10 passes with the new tractor would equal 40" greater cut than the old one. That's 40" = 38" + 2" compared to the old one = one pass across the yard. That's equivalent to I can do in ten passes with the new mower (plus 2") than what I could do with the old one. Which is about equal to I can do in ten passes with the new mower whereas it would take me 11 passes with the old mower. I calculate my MPG (mile per gallon) every week just to see how the car is doing. How would ya'll solve for MPH? quote:Overmind I was the only one in the class with them all correct. Now what I am getting at is, can I join any of you?Do you frighten your friends or people in general? That is something I have noticed when you are smart. Share this post Link to post Share on other sites

Charles Lindsey Report post Posted March 25, 2003 quote:Tyrn Personally, I hate accounting math...it's black magic if you ask me. Just ask Enron! hehe. Shame on me. Share this post Link to post Share on other sites

Tyrn Report post Posted March 25, 2003 quote:Originally posted by Cmdr Chavik: quote:Tyrn Personally, I hate accounting math...it's black magic if you ask me. Just ask Enron! hehe. Shame on me. LOL! Share this post Link to post Share on other sites

OvermindDL1 Report post Posted March 25, 2003 quote:Originally posted by Cmdr Chavik: quote:Overmind I was the only one in the class with them all correct. Now what I am getting at is, can I join any of you?Do you frighten your friends or people in general? That is something I have noticed when you are smart. I... should probobly not answer that... Share this post Link to post Share on other sites

Tyrn Report post Posted March 25, 2003 quote:Originally posted by Overmind: I... should probobly not answer that... Have them running scared do you? At first, I used to wonder if my copy of the test was missing pages. The scores tended to indicate otherwise; so, I stopped worrying about it. Share this post Link to post Share on other sites

Charles Lindsey Report post Posted March 25, 2003 quote:Tyrn At first, I used to wonder if my copy of the test was missing pages.I'm not THAT good. I'm jealous of you Tyrn. Share this post Link to post Share on other sites

Rico Jansen Report post Posted March 25, 2003 Personally, I'm far better at juggling formulas than number crunching. I'm bound to make mistakes at that. Though there's allways the occasional 'sign' that gets lost somehow. Just to put my mind at ease, that first addition was 21,000 right? Share this post Link to post Share on other sites

OvermindDL1 Report post Posted March 25, 2003 22005 I think Share this post Link to post Share on other sites

Tyrn Report post Posted March 25, 2003 quote:Originally posted by Cmdr Chavik: I'm not THAT good. I'm jealous of you Tyrn. Don't be, while I'm still "fast" I can't function without a good textbook for reference as I just don't have a need for most of it any more. Share this post Link to post Share on other sites