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6% compounded yearly for 4 years with principal 20000. We see that 6% interest will make the principal double every 12 years (by the law of 72). But we only need 4 years, so with no more estimation we would need to know <math>2^{1/3}</math>. We estimate this with the above linear equations. So we want to multiply the principal, 20000, by (<math>1 + .8/3</math>). We end up getting 25336. And there ya go! Actual answer: 25250 (less than 1% off ... actually .3%) | 6% compounded yearly for 4 years with principal 20000. We see that 6% interest will make the principal double every 12 years (by the law of 72). But we only need 4 years, so with no more estimation we would need to know <math>2^{1/3}</math>. We estimate this with the above linear equations. So we want to multiply the principal, 20000, by (<math>1 + .8/3</math>). We end up getting 25336. And there ya go! Actual answer: 25250 (less than 1% off ... actually .3%) | ||
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| + | Starting a [[K-12 Proofs and Comments]] page. | ||
Latest revision as of 01:47, 10 May 2016
My Contributions:
Divisibility rules: for 7
Rule 3: "Tail-End divisibility." Note. This only tells you if it is divisible and NOT the remainder. Take a number say 12345. Look at the last digit and add or subtract a multiple of 7 to make it zero. In this case we get 12370 or 12310. Lop off the ending 0's and repeat. 1237 ==> 123 ==> 130 ==> 13 NOPE. Works in general with numbers that are relatively prime to the base (and works GREAT in binary).
Contributions On This Page Only:
Estimating Compound Interest
Look up and understand the "Rule of 72." My short synopsis here says that certain small percentages, say n%, will double in "72 divided by n" years.
I will now estimate 
between x=0 and x=1 by forming segments between the previous x values and x=.5. So for x<.5 we use 1 + .8x and otherwise 1.2x + .8.
I will now give an example of this method!
6% compounded yearly for 4 years with principal 20000. We see that 6% interest will make the principal double every 12 years (by the law of 72). But we only need 4 years, so with no more estimation we would need to know 
. We estimate this with the above linear equations. So we want to multiply the principal, 20000, by (
). We end up getting 25336. And there ya go! Actual answer: 25250 (less than 1% off ... actually .3%)
Starting a K-12 Proofs and Comments page.
