Subject: Re: {GRP} *SUBHAN ALLAH* ~ سبحان الله ~ Please Try This & See ~{!!!}
From: iqbalsheikh@hotmail.com
Date: Tue, 2 Sep 2014 08:44:24 -0400
To: alaaabosamra33@hotmail.com
CC: nurie786@yahoo.com; fisabilillah_alhamdullilah@yahoo.com; hassanfahmy54@hotmail.com; basmaabdelazeam@hotmail.com; mfw1000@gmail.com; dali.dola@yahoo.fr; nanoshkh@yahoo.com; ahmed-chalabi@googlegroups.com; school-of-friendz@googlegroups.com; alwayz2gather@yahoogroups.com; vu-and-company@googlegroups.com; dare-arqam-vu@googlegroups.com; vu-club@googlegroups.com; amalyelgana2@gmail.com; roromuhammad@yahoo.com; news@misr25.com; latif.m.chaudhery@gmail.com; global-right-path@googlegroups.com; ashrafmg@hotmail.com; discuss_islam_the_religion@yahoogroups.com; islamhelptalk@yahoogroups.com; vuclub.net@gmail.com; anata25@ymail.com
Sir/madam,
Please don't be foolish. What about who born in 2000?
Read this carefully:
Compound interest is a simple but very useful rule: The number of years for money to double at annually compounded interest is approximately 72 divided by the interest rate. This simple relationship tell us that for $1 to become $2 it takes about:
36 years at i=2%
18 years at i=4%
12 years at i=6%
9 years at i=8%
6 years at i=12%
4 years at i=18%
This is called "rule of 72". The derivation of this rule is:
If (1+i)n=2
n.log (1+i) = log 2
n=log 2/log(1+i) = .693/δ = .693/i.i/δ
But i/δ is very close to 1+i/2 and at 8% is approximately 1.04.
Then n approx.= .693 (1.04)/i approx.= 72/100i
Hence the rule gives almost exact result at i=.08. For greater accuracy the 72 should be increased or decreased by 1% for each 2% that the rate of interest exceeds or less than 8%.
Note that 72 is easily divisible by 2,3,4,6,8,9 and 12, and hence the rule gives quick and easy answer for many of common interest rates. Except for its limited applicability, the rule of 72 leaves little to be desired.
A similar derivation, but replacing the factor 2 by first 3 and then 5, quickly leads to the "rule of 114"for tripling and the "rule of 167" for a five-fold increase. If we let the "magic number" for an increase by a factor of f be represented by MNf, and be calculated by 104 log f, we can apply the usual rules for manipulating logarithms and come up with the following:
f MNf (MN means Magic Number)
2 72
3 114
4 144 = 72 + 72
8 216 = 72 + 72 + 72
9 228 = 114 + 114
10 239 = 72 + 167
12 258 = 114 + 144
Note that once we know that 72, 114, and 167 are the magic numbers for f = 2, 3, and 5, we have little further use of a log table, since the values of MNf for all other integers up to 12 (the prime numbers 7 and 11 being exceptions) can be obtained by combination. The MNf for some fractional values of f are easily found; e.g MN2.5 = MN5 – MN2 =95. Still other values of MNf can be obtained by interpolation. Linear interpolation in a log table is reasonably accurate if the log is not to close to zero.
Once one has memorized the number 72, 114, and 167, and has mastered the technique for finding other MNfvalues, his range of application is extended. Given any two of i, n, and f, the third can be approximated, with recourse to mental arithmetic only. Examples:
(1)How long does it take for a dollar at 10% interest to increase by a factor of 10?
Ans: (72 + 167)/10 = 24 Years approx.
(2) At what interest rate does $1 become $8 after 36 years?
Ans: (72 + 72 + 72)/36 = 6%
(3) By what factor will a dollar invested at 9.5% for 15 years have increased?
Ans: MNf - 15 . 9.5 - 142.5. MN4 – 144. The required factor is approximately 4.
These examples so far given come from the theory of interest, the magic numbers are equally useful in calculations involving other forms of exponential growth.
(4) How long will it take for a population growing at a 1.5% annually rate to triple?
Ans: 114/1.5 – 76 years, approximately. Here we can improve the approximation by dividing by 1.0325, to recognize that 1.5% growth rate is rather far from 8%. 76/1.0325 = 73.6.
(5) If a corporation's sales have increased 10-fold in 20 years, what is the average annual rate of sales growth?
Ans: (167 + 72)/20 = 12%. Here we know that our first approximation is a bit low, because the MNfs at 12% should be 2% higher. 12 (1.02) =12.25%.
Those who like to solve problems involving exponential growth at constant rate, without use of interest tables, logarithms, or calculators, will find much of value in the three magic numbers 72, 114, 167. Learn to use them and amaze your friends:)!
Sent from my iPhone
Allah save all muslims and get us free
Date: Sun, 31 Aug 2014 20:16:07 -0700
From: global-right-path@googlegroups.com
Subject: {GRP} *SUBHAN ALLAH* ~ سبحان الله ~ Please Try This & See ~{!!!}
To: fisabilillah_alhamdullilah@yahoo.com
The Sunnah in my Heart, Allah on my Mind,
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