Handicap principle: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
Newer edit →
en>YFdyh-bot
m r2.7.3) (Robot: Adding ar:قاعدة التعويق
 
en>BattyBot
m fixed CS1 errors: dates & General fixes using AWB (9832)
Line 1: Line 1:
It is very common to have a dental emergency -- a fractured tooth, an abscess, or severe pain when chewing. Over-the-counter pain medication is just masking the problem. Seeing an emergency dentist is critical to getting the source of the problem diagnosed and corrected as soon as possible.<br><br>Here are some common dental emergencies:<br>Toothache: The most common dental emergency. This generally means a badly decayed tooth. As the pain affects the tooth's nerve, treatment involves gently removing any debris lodged in the cavity being careful not to poke deep as this will cause severe pain if the nerve is touched. Next rinse vigorously with warm water. Then soak a small piece of cotton in oil of cloves and insert it in the cavity. This will give temporary relief until a dentist can be reached.<br><br>At times the pain may have a more obscure location such as decay under an old filling. As this can be only corrected by a dentist there are two things you can do to help the pain. Administer a pain pill (aspirin or some other analgesic) internally or dissolve a tablet in a half glass (4 oz) of warm water holding it in the mouth for several minutes before spitting it out. DO NOT PLACE A WHOLE TABLET OR ANY PART OF IT IN THE TOOTH OR AGAINST THE SOFT GUM TISSUE AS IT WILL RESULT IN A NASTY BURN.<br><br>Swollen Jaw: This may be caused by several conditions the most probable being an abscessed tooth. In any case the treatment should be to reduce pain and swelling. An ice pack held on the outside of the jaw, (ten minutes on and ten minutes off) will take care of both. If this does not control the pain, an analgesic tablet can be given every four hours.<br><br>Other Oral Injuries: Broken teeth, cut lips, bitten tongue or lips if severe means a trip to a dentist as soon as possible. In the mean time rinse the mouth with warm water and place cold compression the face opposite the injury. If there is a lot of bleeding, apply direct pressure to the bleeding area. If bleeding does not stop get patient to the emergency room of a hospital as stitches may be necessary.<br><br>Prolonged Bleeding Following Extraction: Place a gauze pad or better still a moistened tea bag over the socket and have the patient bite down gently on it for 30 to 45 minutes. The tannic acid in the tea seeps into the tissues and often helps stop the bleeding. If bleeding continues after two hours, call the dentist or take patient to the emergency room of the nearest hospital.<br><br>Broken Jaw: If you suspect the patient's jaw is broken, bring the upper and lower teeth together. Put a necktie, handkerchief or towel under the chin, tying it over the head to immobilize the jaw until you can get the patient to a dentist or the emergency room of a hospital.<br><br>Painful Erupting Tooth: In young children teething pain can come from a loose baby tooth or from an erupting permanent tooth. Some relief can be given by crushing a little ice and wrapping it in gauze or a clean piece of cloth and putting it directly on the tooth or gum tissue where it hurts. The numbing effect of the cold, along with an appropriate dose of aspirin, usually provides temporary relief.<br><br>In young adults, an erupting 3rd molar (Wisdom tooth), especially if it is impacted, can cause the jaw to swell and be quite painful. Often the gum around the tooth will show signs of infection. Temporary relief can be had by giving aspirin or some other painkiller and by dissolving an aspirin in half a glass of warm water and holding this solution in the mouth over the sore gum. AGAIN DO NOT PLACE A TABLET DIRECTLY OVER THE GUM OR CHEEK OR USE THE ASPIRIN SOLUTION ANY STRONGER THAN RECOMMENDED TO PREVENT BURNING THE TISSUE. The swelling of the jaw can be reduced by using an ice pack on the outside of the face at intervals of ten minutes on and ten minutes off.<br><br>Here's more info in regards to [http://www.youtube.com/watch?v=90z1mmiwNS8 Dentists in DC] have a look at our web site.
In [[finance]], the '''rule of 72''', the '''rule of 70''' and the '''rule of 69''' are methods for estimating an [[investment]]'s doubling time. The rule number (e.g., 72) is divided by the interest percentage per period to obtain the approximate number of periods (usually years) required for doubling.  Although [[scientific calculator]]s and [[spreadsheet]] programs have functions to find the accurate doubling time, the rules are useful for [[mental calculation]]s and when only a basic [[calculator]] is available.<ref>{{Cite book|title=All the Math You'll Ever Need|author=Slavin, Steve|publisher=[[John Wiley & Sons]]|year=1989|isbn=0-471-50636-2|pages=153–154}}</ref>
 
These rules apply to [[exponential growth]] and are therefore used for [[compound interest]] as opposed to [[simple interest]] calculations. They can also be used for [[exponential decay|decay]] to obtain a halving time. The choice of number is mostly a matter of preference, 69 is more accurate for continuous compounding, while 72 works well in common interest situations and is more easily divisible.
There are a number of variations to the rules that improve accuracy. For periodic compounding, the ''exact'' doubling time for an interest rate of ''r'' per period is
:<math>T = \frac{\ln(2)}{\ln(1+r)}</math>,
where ''T'' is the number of periods required. The formula above can be used for more than calculating the doubling time.  If you want to know the tripling time, for example, simply replace the constant 2 in the numerator with 3.  As another example, if you want to know the number of periods it takes for the initial value to rise by 50%, replace the constant 2 with 1.5.
 
== Using the rule to estimate compounding periods ==
 
To estimate the number of periods required to double an original investment, divide the most convenient "rule-quantity" by the expected growth rate, expressed as a percentage.
*For instance, if you were to invest $100 with compounding interest at a rate of 9% per annum, the rule of 72 gives 72/9 = 8 years required for the investment to be worth $200; an exact calculation gives ln(2)/ln(1+.09) = 8.0432 years.
 
Similarly, to determine the time it takes for the value of money to halve at a given rate, divide the rule quantity by that rate.
 
*To determine the time for [[money]]'s [[Purchasing power|buying power]] to halve, financiers simply divide the rule-quantity by the [[inflation rate]]. Thus at 3.5% [[inflation]] using the '''rule of 70''', it should take approximately 70/3.5 = 20 years for the value of a unit of currency to halve.
 
*To estimate the impact of additional fees on financial policies (e.g., [[mutual fund fees and expenses]], loading and expense charges on [[variable universal life insurance]] investment portfolios), divide 72 by the fee. For example, if the Universal Life policy charges a 3% fee over and above the cost of the underlying investment fund, then the total account value will be cut to 1/2 in 72 / 3 = 24 years, and then to just 1/4 the value in 48 years, compared to holding exactly the same investment outside the policy.
 
== Choice of rule ==
The value 72 is a convenient choice of numerator, since it has many small [[divisor]]s: 1, 2, 3, 4, 6, 8, 9, and 12. It provides a good approximation for annual compounding, and for compounding at typical rates (from 6% to 10%). The approximations are less accurate at higher interest rates.
 
For continuous compounding, 69 gives accurate results for any rate. This is because [[natural logarithm|ln]](2) is about 69.3%; see derivation below. Since daily compounding is close enough to continuous compounding, for most purposes 69, 69.3 or 70 are better than 72 for daily compounding. For lower annual rates than those above, 69.3 would also be more accurate than 72.
 
{| class="wikitable sortable"
! Rate
! Actual Years
! Rule of 72
! Rule of 70
! Rule of 69.3
! 72 adjusted
! E-M rule
|-
| 0.25% || 277.605 || 288.000 || 280.000 || 277.200 || 277.667 || 277.547
|-
| 0.5% || 138.976 || 144.000 || 140.000 || 138.600 || 139.000 || 138.947
|-
| 1% || 69.661 || 72.000 || 70.000 || 69.300 || 69.667 || 69.648
|-
| 2% || 35.003 || 36.000 || 35.000 || 34.650 || 35.000 || 35.000
|-
| 3% || 23.450 || 24.000 || 23.333 || 23.100 || 23.444 || 23.452
|-
| 4% || 17.673 || 18.000 || 17.500 || 17.325 || 17.667 || 17.679
|-
| 5% || 14.207 || 14.400 || 14.000 || 13.860 || 14.200 || 14.215
|-
| 6% || 11.896 || 12.000 || 11.667 || 11.550 || 11.889 || 11.907
|-
| 7% || 10.245 || 10.286 || 10.000 || 9.900 || 10.238 || 10.259
|-
| 8% || 9.006 || 9.000 || 8.750 || 8.663 || 9.000 || 9.023
|-
| 9% || 8.043 || 8.000 || 7.778 || 7.700 || 8.037 || 8.062
|-
| 10% || 7.273 || 7.200 || 7.000 || 6.930 || 7.267 || 7.295
|-
| 11% || 6.642 || 6.545 || 6.364 || 6.300 || 6.636 || 6.667
|-
| 12% || 6.116 || 6.000 || 5.833 || 5.775 || 6.111 || 6.144
|-
| 15% || 4.959 || 4.800 || 4.667 || 4.620 || 4.956 || 4.995
|-
| 18% || 4.188 || 4.000 || 3.889 || 3.850 || 4.185 || 4.231
|-
| 20% || 3.802 || 3.600 || 3.500 || 3.465 || 3.800 || 3.850
|-
| 25% || 3.106 || 2.880 || 2.800 || 2.772 || 3.107 || 3.168
|-
| 30% || 2.642 || 2.400 || 2.333 || 2.310 || 2.644 || 2.718
|-
| 40% || 2.060 || 1.800 || 1.750 || 1.733 || 2.067 || 2.166
|-
| 50% || 1.710 || 1.440 || 1.400 || 1.386 || 1.720 || 1.848
|-
| 60% || 1.475 || 1.200 || 1.167 || 1.155 || 1.489 || 1.650
|-
| 70% || 1.306 || 1.029 || 1.000 || 0.990 || 1.324 || 1.523
|}'''
 
==History==
An early reference to the rule is in the ''[[Fra_Luca_Pacioli#Work|Summa de Arithmetica]]'' (Venice, 1494. Fol. 181, n. 44) of [[Luca Pacioli]] (1445–1514). He presents the rule in a discussion regarding the estimation of the doubling time of an investment, but does not derive or explain the rule, and it is thus assumed that the rule predates Pacioli by some time.
{{cquote|'' A voler sapere ogni quantita a tanto per 100 l'anno, in quanti anni sarà tornata doppia tra utile e capitale, '''tieni per regola 72''', a mente, il quale sempre partirai per l'interesse, e quello che ne viene, in tanti anni sarà raddoppiato. Esempio: Quando l'interesse è a 6 per 100 l'anno, dico che si parta 72 per 6; ne vien 12, e in 12 anni sarà raddoppiato il capitale.'' (emphasis added).}}
Roughly translated:
{{cquote|In wanting to know of any capital, at a given yearly percentage, in how many years it will double adding the interest to the capital, '''keep as a rule [the number] 72''' in mind, which you will always divide by the interest, and what results, in that many years it will be doubled. Example: When the interest is 6 percent per year, I say that one divides 72 by 6; 12 results, and in 12 years the capital will be doubled.}}
 
==Adjustments for higher accuracy==
For higher rates, a bigger [[numerator]] would be better (e.g., for 20%, using 76 to get 3.8 years would be only about 0.002 off, where using 72 to get 3.6 would be about 0.2 off).  This is because, as above, the rule of 72 is only an approximation that is accurate for interest rates from 6% to 10%. Outside that range the error will vary from 2.4% to −14.0%. For every three percentage points away from 8% the value 72 could be adjusted by 1.
 
:<math> t \approx \frac{72 + (r - 8)/3}{r} </math>
 
or for the same result, but simpler:
 
:<math> t \approx \frac{70 + (r - 2)/3}{r} </math>
:<math> t \approx \frac{69.3}{r} + 0.33</math>
 
===E-M rule===
The Eckart-McHale second-order rule, the E-M rule, provides a multiplicative correction for the Rule of 69.3 that is very accurate for rates from 0%–20%. The Rule of 69.3 is normally only accurate at the lowest end of interest rates, from 0% to about 5%. To compute the E-M approximation, simply multiply the Rule of 69.3 result by 200/(200-''r'') as follows:
 
:<math> t \approx \frac{69.3}{r} \times \frac{200}{200-r}</math>
 
For example, if the interest rate is 18% the Rule of 69.3 says ''t'' = 3.85 years. The E-M Rule multiplies this by 200/(200-18), giving a doubling time of 4.23 years, where the actual doubling time at this rate is 4.19 years. (The E-M Rule thus gives a closer approximation than the Rule of 72.)
 
Note that if the numerator here is simply 69.3 times 200.  As long as the product stays constant, the factors can be modified arbitrarily. The E-M rule could thus be written also as
 
:<math> t \approx \frac{70}{r} \times \frac{198}{200-r}</math> or <math> t \approx \frac{72}{r} \times \frac{192}{200-r}</math>
 
in order to keep the product mostly unchanged.  In these variants, the multiplicative correction becomes 1 respectively for r=2 and r=8, the values for which the rule of 70 (respectively 72) is most precise.
 
Similarly, the 3rd-order [[Padé approximant]] gives a more accurate answer over an even larger range of ''r'', but it has a slightly more complicated formula:
 
:<math> t \approx \frac{69.3}{r} \times \frac{600+4r}{600+r}</math>
 
== Other rules ==
Extending the rule of 72 out further, other approximations can be determined for tripling and quadrupling. To estimate the time it would take to triple your money, one can use 114 instead of 72 and, for quadrupling, use 144.
 
==Derivation==
===Periodic compounding ===
For [[Compound interest#Periodic compounding|periodic compounding]], [[future value]] is given by:
:<math>FV = PV \cdot (1+r)^t</math>
where <math>PV</math> is the [[present value]], <math>t</math> is the number of time periods, and <math>r</math> stands for the interest rate per time period.
 
The future value is double the present value when the following condition is met:
:<math>(1+r)^t = 2\,</math>
This equation is easily solved for <math>t</math>:
:<math>
  \begin{array}{ccc}
            \ln((1+r)^t) & = & \ln 2                  \\
    t \cdot \ln(1+r)  & = & \ln 2                  \\
    t                  & = & \frac{\ln 2}{\ln(1+r)}
  \end{array}
</math>
If ''r'' is small, then ln(1 + ''r'') [[Natural_logarithm#Derivative.2C_Taylor_series|approximately equals ''r'']] (this is the first term in the [[Taylor series#Calculation of Taylor series|Taylor series]]). Together with the approximation <math>ln(2) \approx 0.693147</math>, this gives:
:<math>t \approx \frac{0.693147}{r}</math>
which improves in accuracy as the [[Compound Interest|compounding of interest]] becomes continuous (see derivation below).
 
However, humans tend to prefer performing mental calculations with [[percentage]]s, so the formula is often restated as follows:
:<math>
  \begin{array}{ccc}
    t & \approx & \frac{0.693147}{r}              \\ & & \\
      &    =    & \frac{0.693147}{R%}              \\ & & \\
      &    =    & \frac{0.693147}{R \frac{1}{100}} \\ & & \\
      &    =    & \frac{0.693147 \cdot 100}{R}    \\ & & \\
      &    =    & \frac{69.3147}{R}                \\ & & \\
      & \approx & \frac{70}{R}
  \end{array}
</math>
 
In order to derive the more precise adjustments presented above, it is noted that <math>\ln(1+r)\,</math> is more closely approximated by <math>r - \frac{r^2}{2}</math> (using the second term in the [[Taylor Series|Taylor series]]). <math>\frac{0.693}{r - r^2/2}</math> can then be further simplified by Taylor approximations:
 
:<math>
  \begin{array}{ccc}
    \frac{0.693}{r - r^2/2} & = & \frac{69.3}{R - R^2/200} \\  & & \\
      &    =    & \frac{69.3}{R}    \frac{1}{1-R/200}      \\  & & \\
      & \approx & \frac{69.3 (1+R/200)}{R}                \\  & & \\
      &    =    & \frac{69.3}{R}+\frac{69.3}{200}          \\  & & \\
      &    =    & \frac{69.3}{R}+0.34\end{array}
</math>
 
Replacing the "R" in ''R/200'' on the third line with 7.79 gives 72 on the numerator.  This shows that the rule of 72 is most precise for periodically composed interests around 8%.
 
Alternatively, the E-M rule is obtained if the second-order Taylor approximation is used directly.
 
=== Continuous compounding ===
For [[Compound interest#Continuous compounding|continuous compounding]], the derivation is simpler:
:<math>
  \begin{array}{ccc}
        (e^r)^p &    =    &          2        \\
        e^{rp}  &    =    &          2        \\
    \ln e^{rp}  &    =    &      \ln 2        \\
          rp  &    =    &      \ln 2        \\
            p  &    =    & \frac{\ln 2}{r}    \\
                &        &                    \\
            p  & \approx & \frac{0.693147}{r}
  \end{array}
</math>
 
==See also==
 
* [[Exponential growth]]
* [[Time value of money]]
* [[Interest]]
* [[Discounting|Discount]]
* [[Volatility (finance)|Rule of 16]]
 
== References ==
{{Reflist}}
 
==External links==
* [http://members.optusnet.com.au/exponentialist/The_Scales_Of_70.htm The Scales Of 70] –  extends the rule of 72 beyond fixed-rate growth to variable rate compound growth including positive and negative rates.
*[http://www.iassa.co.za/articles/003_nov1973_05.pdf A note on the rule of 72 or how long it takes to double your money], [[Investment Analysts Society of Southern Africa|The Investment Analysts Society of South Africa]]
*[http://www.moneychimp.com/features/rule72.htm Rule of 72 Calculator], moneychimp.com
*[http://www.directinvesting.com/drip_learning_center/rule_of_72.cfm Rule of 72 Learning Tool], directinvesting.com
*[http://www.excelexchange.com/discount%20mathematics.htm Financial Mathematics], ExcelExchange
 
{{DEFAULTSORT:Rule Of 72}}
[[Category:Debt]]
[[Category:Exponentials]]
[[Category:Interest]]
[[Category:Rules of thumb]]
[[Category:Mathematical finance]]

Revision as of 23:52, 5 January 2014

In finance, the rule of 72, the rule of 70 and the rule of 69 are methods for estimating an investment's doubling time. The rule number (e.g., 72) is divided by the interest percentage per period to obtain the approximate number of periods (usually years) required for doubling. Although scientific calculators and spreadsheet programs have functions to find the accurate doubling time, the rules are useful for mental calculations and when only a basic calculator is available.[1]

These rules apply to exponential growth and are therefore used for compound interest as opposed to simple interest calculations. They can also be used for decay to obtain a halving time. The choice of number is mostly a matter of preference, 69 is more accurate for continuous compounding, while 72 works well in common interest situations and is more easily divisible. There are a number of variations to the rules that improve accuracy. For periodic compounding, the exact doubling time for an interest rate of r per period is

T=ln⁡(2)ln⁡(1+r),

where T is the number of periods required. The formula above can be used for more than calculating the doubling time. If you want to know the tripling time, for example, simply replace the constant 2 in the numerator with 3. As another example, if you want to know the number of periods it takes for the initial value to rise by 50%, replace the constant 2 with 1.5.

Using the rule to estimate compounding periods

To estimate the number of periods required to double an original investment, divide the most convenient "rule-quantity" by the expected growth rate, expressed as a percentage.

  • For instance, if you were to invest $100 with compounding interest at a rate of 9% per annum, the rule of 72 gives 72/9 = 8 years required for the investment to be worth $200; an exact calculation gives ln(2)/ln(1+.09) = 8.0432 years.

Similarly, to determine the time it takes for the value of money to halve at a given rate, divide the rule quantity by that rate.

  • To determine the time for money's buying power to halve, financiers simply divide the rule-quantity by the inflation rate. Thus at 3.5% inflation using the rule of 70, it should take approximately 70/3.5 = 20 years for the value of a unit of currency to halve.
  • To estimate the impact of additional fees on financial policies (e.g., mutual fund fees and expenses, loading and expense charges on variable universal life insurance investment portfolios), divide 72 by the fee. For example, if the Universal Life policy charges a 3% fee over and above the cost of the underlying investment fund, then the total account value will be cut to 1/2 in 72 / 3 = 24 years, and then to just 1/4 the value in 48 years, compared to holding exactly the same investment outside the policy.

Choice of rule

The value 72 is a convenient choice of numerator, since it has many small divisors: 1, 2, 3, 4, 6, 8, 9, and 12. It provides a good approximation for annual compounding, and for compounding at typical rates (from 6% to 10%). The approximations are less accurate at higher interest rates.

For continuous compounding, 69 gives accurate results for any rate. This is because ln(2) is about 69.3%; see derivation below. Since daily compounding is close enough to continuous compounding, for most purposes 69, 69.3 or 70 are better than 72 for daily compounding. For lower annual rates than those above, 69.3 would also be more accurate than 72.

Rate Actual Years Rule of 72 Rule of 70 Rule of 69.3 72 adjusted E-M rule
0.25% 277.605 288.000 280.000 277.200 277.667 277.547
0.5% 138.976 144.000 140.000 138.600 139.000 138.947
1% 69.661 72.000 70.000 69.300 69.667 69.648
2% 35.003 36.000 35.000 34.650 35.000 35.000
3% 23.450 24.000 23.333 23.100 23.444 23.452
4% 17.673 18.000 17.500 17.325 17.667 17.679
5% 14.207 14.400 14.000 13.860 14.200 14.215
6% 11.896 12.000 11.667 11.550 11.889 11.907
7% 10.245 10.286 10.000 9.900 10.238 10.259
8% 9.006 9.000 8.750 8.663 9.000 9.023
9% 8.043 8.000 7.778 7.700 8.037 8.062
10% 7.273 7.200 7.000 6.930 7.267 7.295
11% 6.642 6.545 6.364 6.300 6.636 6.667
12% 6.116 6.000 5.833 5.775 6.111 6.144
15% 4.959 4.800 4.667 4.620 4.956 4.995
18% 4.188 4.000 3.889 3.850 4.185 4.231
20% 3.802 3.600 3.500 3.465 3.800 3.850
25% 3.106 2.880 2.800 2.772 3.107 3.168
30% 2.642 2.400 2.333 2.310 2.644 2.718
40% 2.060 1.800 1.750 1.733 2.067 2.166
50% 1.710 1.440 1.400 1.386 1.720 1.848
60% 1.475 1.200 1.167 1.155 1.489 1.650
70% 1.306 1.029 1.000 0.990 1.324 1.523

History

An early reference to the rule is in the Summa de Arithmetica (Venice, 1494. Fol. 181, n. 44) of Luca Pacioli (1445–1514). He presents the rule in a discussion regarding the estimation of the doubling time of an investment, but does not derive or explain the rule, and it is thus assumed that the rule predates Pacioli by some time. Benefits of Living in a Rental or Landed property in Singapore Property New Launches & Undertaking Showcase In Singapore Many residential Singapore property gross sales contain shopping for property in Singapore at new launches. These are often properties below development, being sold new by developers. New Launch Singapore Property, 28 Imperial Residences Coming To Geylang Lorong 26 The property market is slowing down, in accordance with personal property transactions in Could Cellular Apps FREE Signal Up Log in Property Agents Feedback

Banks usually engage skilled valuers to conduct valuations of properties. The valuers are required to abide by industry requirements and guidelines for property valuation prescribed by the Singapore Institute of Surveyors and Valuers. With Singapore conserving its greenery and with town sky view being the attraction to many, it is no wonder that increasingly condos are being developed on the island. Many future traders are placing extra value on units with a view than these with out one. Thus, this may be one of the reasons too as to why your unit of selection is either with a view or with out. How to Spot Abroad Property Scams (at Propwise.sg) New Condominium Eco Sanctuary Launch 01Dec 2012 Coming Quickly !!! New launch rental COCO Palm at Pasir Ris

Association charges has to be paid by each condominium proprietor, weather you are dwelling in it or not, or even in case you have rented the property. So, whether you employ the amenities and amenities at the condominium, you'll any how must pay for them. JOHOR BAHARU, Jan 22 (Bernama) — The property market in Johor Baharu and Iskandar Malaysia has been negatively affected by the cooling measures introduced by the authorities to address rising property prices, says the Actual Property and Housing Developers' Association of Malaysia (Rehda). District 18, 99 years LH Executive Apartment District 25, ninety nine years LH Executive Rental District 19, ninety nine years LH Government Apartment pipelines. Property homeowners haven't any different but to pay up. There's no different sensible Hottest Launch D'Leedon

Dr Victor Lee is a surgeon gazetted to carry out multi-organ transplant surgical procedure. He underwent his fellowship coaching in transplant surgery on the Royal Infirmary of Edinburgh, United Kingdom in 2008 and 2009. He is presently a consultant surgeon at the Singapore Normal Hospital, and visiting guide to the National College Hospital. His scientific interest and skills are in the areas of transplant surgery, hepatobiliary pancreatic surgery and laparoscopic surgical procedure.

Lush Acres Government Condominium goes to launch quickly at Sengkang West Method By Metropolis Developments Limited. Lush Acres reflects the large expense of house, environmentally-inexperienced constructing and plush panorama of this low density development with solely 22% of website protection. There have been students, retirees and property agents napping, snacking and taking part in cards within the queue to kill time. Such a scene made passers-by wonder if the gang really consisted of genuine consumers, or just part-timers being paid to fake how sizzling the new undertaking was. The model was filed in Switzerland in October 2009 with a model r egistration dated March 25, 2010 A deposit was also recorded in France at the INPI (National Institute of Intellectual Property) Coastal commercial spaceports

Individuals all wish to be seen having the identical foresight because the specialists in property investment or the massive names in their own fields. Thus the discharge of these tales works to motivate other patrons to follow go well with. Bartley Ridge is the hottest new launch in district 13. Irresistible pricing from $1,1xx psf. Bartley Ridge is a ninety nine-yr leasehold new condo at Mount Vernon highway, excellent subsequent to Bartley MRT station (CC12). If you wish to get more Rehda Johor chairman Koh Moo Hing stated potential property patrons within the two areas at the moment are adopting a wait-and-see angle. How can I get the ebrochure and flooring plans of the new launch initiatives ? The Current Mortgage to your HDB District thirteen, Freehold condominium District 11, Freehold Cluster landed house Sea Horizon EC @ Pasir Ris

The simplest way is to contact a real estate agent who's a Advertising Workforce Member The agent will doubtless meet to show you details of the undertaking supplied by the developer. Attending a preview doesn't suggest you are obliged to purchase a unit. You can select not to and your cheque will likely be returned to you. No cost concerned. Your cheque will likely be returned to you in the event you decide to not proceed to purchase. Early hen low cost (up to 10%) at the preview earlier than the official launch. The purpose of that is to stimulate demand and to create a buying house in singapore momentum. As soon as this function is achieved, the developer would then take away the low cost so as to maximize his profitability. 2/3/4 bedrooms units obtainable ! GREATEST PURCHASE NOW !!! AVG $1900psf The Key Commercial Cluster in the North Area Roughly translated: Benefits of Living in a Rental or Landed property in Singapore Property New Launches & Undertaking Showcase In Singapore Many residential Singapore property gross sales contain shopping for property in Singapore at new launches. These are often properties below development, being sold new by developers. New Launch Singapore Property, 28 Imperial Residences Coming To Geylang Lorong 26 The property market is slowing down, in accordance with personal property transactions in Could Cellular Apps FREE Signal Up Log in Property Agents Feedback

Banks usually engage skilled valuers to conduct valuations of properties. The valuers are required to abide by industry requirements and guidelines for property valuation prescribed by the Singapore Institute of Surveyors and Valuers. With Singapore conserving its greenery and with town sky view being the attraction to many, it is no wonder that increasingly condos are being developed on the island. Many future traders are placing extra value on units with a view than these with out one. Thus, this may be one of the reasons too as to why your unit of selection is either with a view or with out. How to Spot Abroad Property Scams (at Propwise.sg) New Condominium Eco Sanctuary Launch 01Dec 2012 Coming Quickly !!! New launch rental COCO Palm at Pasir Ris

Association charges has to be paid by each condominium proprietor, weather you are dwelling in it or not, or even in case you have rented the property. So, whether you employ the amenities and amenities at the condominium, you'll any how must pay for them. JOHOR BAHARU, Jan 22 (Bernama) — The property market in Johor Baharu and Iskandar Malaysia has been negatively affected by the cooling measures introduced by the authorities to address rising property prices, says the Actual Property and Housing Developers' Association of Malaysia (Rehda). District 18, 99 years LH Executive Apartment District 25, ninety nine years LH Executive Rental District 19, ninety nine years LH Government Apartment pipelines. Property homeowners haven't any different but to pay up. There's no different sensible Hottest Launch D'Leedon

Dr Victor Lee is a surgeon gazetted to carry out multi-organ transplant surgical procedure. He underwent his fellowship coaching in transplant surgery on the Royal Infirmary of Edinburgh, United Kingdom in 2008 and 2009. He is presently a consultant surgeon at the Singapore Normal Hospital, and visiting guide to the National College Hospital. His scientific interest and skills are in the areas of transplant surgery, hepatobiliary pancreatic surgery and laparoscopic surgical procedure.

Lush Acres Government Condominium goes to launch quickly at Sengkang West Method By Metropolis Developments Limited. Lush Acres reflects the large expense of house, environmentally-inexperienced constructing and plush panorama of this low density development with solely 22% of website protection. There have been students, retirees and property agents napping, snacking and taking part in cards within the queue to kill time. Such a scene made passers-by wonder if the gang really consisted of genuine consumers, or just part-timers being paid to fake how sizzling the new undertaking was. The model was filed in Switzerland in October 2009 with a model r egistration dated March 25, 2010 A deposit was also recorded in France at the INPI (National Institute of Intellectual Property) Coastal commercial spaceports

Individuals all wish to be seen having the identical foresight because the specialists in property investment or the massive names in their own fields. Thus the discharge of these tales works to motivate other patrons to follow go well with. Bartley Ridge is the hottest new launch in district 13. Irresistible pricing from $1,1xx psf. Bartley Ridge is a ninety nine-yr leasehold new condo at Mount Vernon highway, excellent subsequent to Bartley MRT station (CC12). If you wish to get more Rehda Johor chairman Koh Moo Hing stated potential property patrons within the two areas at the moment are adopting a wait-and-see angle. How can I get the ebrochure and flooring plans of the new launch initiatives ? The Current Mortgage to your HDB District thirteen, Freehold condominium District 11, Freehold Cluster landed house Sea Horizon EC @ Pasir Ris

The simplest way is to contact a real estate agent who's a Advertising Workforce Member The agent will doubtless meet to show you details of the undertaking supplied by the developer. Attending a preview doesn't suggest you are obliged to purchase a unit. You can select not to and your cheque will likely be returned to you. No cost concerned. Your cheque will likely be returned to you in the event you decide to not proceed to purchase. Early hen low cost (up to 10%) at the preview earlier than the official launch. The purpose of that is to stimulate demand and to create a buying house in singapore momentum. As soon as this function is achieved, the developer would then take away the low cost so as to maximize his profitability. 2/3/4 bedrooms units obtainable ! GREATEST PURCHASE NOW !!! AVG $1900psf The Key Commercial Cluster in the North Area

Adjustments for higher accuracy

For higher rates, a bigger numerator would be better (e.g., for 20%, using 76 to get 3.8 years would be only about 0.002 off, where using 72 to get 3.6 would be about 0.2 off). This is because, as above, the rule of 72 is only an approximation that is accurate for interest rates from 6% to 10%. Outside that range the error will vary from 2.4% to −14.0%. For every three percentage points away from 8% the value 72 could be adjusted by 1.

t≈72+(r−8)/3r

or for the same result, but simpler:

t≈70+(r−2)/3r
t≈69.3r+0.33

E-M rule

The Eckart-McHale second-order rule, the E-M rule, provides a multiplicative correction for the Rule of 69.3 that is very accurate for rates from 0%–20%. The Rule of 69.3 is normally only accurate at the lowest end of interest rates, from 0% to about 5%. To compute the E-M approximation, simply multiply the Rule of 69.3 result by 200/(200-r) as follows:

t≈69.3r×200200−r

For example, if the interest rate is 18% the Rule of 69.3 says t = 3.85 years. The E-M Rule multiplies this by 200/(200-18), giving a doubling time of 4.23 years, where the actual doubling time at this rate is 4.19 years. (The E-M Rule thus gives a closer approximation than the Rule of 72.)

Note that if the numerator here is simply 69.3 times 200. As long as the product stays constant, the factors can be modified arbitrarily. The E-M rule could thus be written also as

t≈70r×198200−r or t≈72r×192200−r

in order to keep the product mostly unchanged. In these variants, the multiplicative correction becomes 1 respectively for r=2 and r=8, the values for which the rule of 70 (respectively 72) is most precise.

Similarly, the 3rd-order Padé approximant gives a more accurate answer over an even larger range of r, but it has a slightly more complicated formula:

t≈69.3r×600+4r600+r

Other rules

Extending the rule of 72 out further, other approximations can be determined for tripling and quadrupling. To estimate the time it would take to triple your money, one can use 114 instead of 72 and, for quadrupling, use 144.

Derivation

Periodic compounding

For periodic compounding, future value is given by:

FV=PV⋅(1+r)t

where PV is the present value, t is the number of time periods, and r stands for the interest rate per time period.

The future value is double the present value when the following condition is met:

(1+r)t=2

This equation is easily solved for t:

ln⁡((1+r)t)=ln⁡2t⋅ln⁡(1+r)=ln⁡2t=ln⁡2ln⁡(1+r)

If r is small, then ln(1 + r) approximately equals r (this is the first term in the Taylor series). Together with the approximation ln(2)≈0.693147, this gives:

t≈0.693147r

which improves in accuracy as the compounding of interest becomes continuous (see derivation below).

However, humans tend to prefer performing mental calculations with percentages, so the formula is often restated as follows:

t≈0.693147r=0.693147R%=0.693147R1100=0.693147⋅100R=69.3147R≈70R

In order to derive the more precise adjustments presented above, it is noted that ln⁡(1+r) is more closely approximated by r−r22 (using the second term in the Taylor series). 0.693r−r2/2 can then be further simplified by Taylor approximations:

0.693r−r2/2=69.3R−R2/200=69.3R11−R/200≈69.3(1+R/200)R=69.3R+69.3200=69.3R+0.34

Replacing the "R" in R/200 on the third line with 7.79 gives 72 on the numerator. This shows that the rule of 72 is most precise for periodically composed interests around 8%.

Alternatively, the E-M rule is obtained if the second-order Taylor approximation is used directly.

Continuous compounding

For continuous compounding, the derivation is simpler:

(er)p=2erp=2ln⁡erp=ln⁡2rp=ln⁡2p=ln⁡2rp≈0.693147r

See also

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

External links

  1. ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
Retrieved from "https://en.formulasearchengine.com/index.php?title=Handicap_principle&oldid=4076"