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## How should I think about how much I save and how do I allocate when I begin to to build my investment portfolio?

Saving for the future is not a choice or an option but a compulsion. Over the last 40 years, average life expectancy rates[1][1][1][1] have increased at the rate of 5 years per person for every passing decade. But, we know better, as we have many elderly people well into their 80’s, living in good health. Continuing at this rate, by 2040, avg life expectancy can be around 80 years, making it imperative (to increase savings and grow our investments).All of this comes at a cost. Assuming that you currently have an expense of Rs. 100,000 per month, over a 20 year period, with 6% avg inflation, the value of that Rs. 100,000 reduces[2][2][2][2] to only Rs. 31,180.Alternately, to maintain your current standard of living[3][3][3][3] (Rs. 100,000/month) after 20 years with an inflation rate of 6%, you would need Rs. 320,714.This information might not give you the exact monthly expenses after 20 years but one thing is for sure, it is going to be pretty expensive living into the 80s, 90s.In addition, there would be various financial goals between now and till the time you turn 60 or 70 or 80 - education loans, marriage, starting a family, buying a vehicle, house, kids expenses, their education, marriage etc and then comes the retirement goals. To meet all these expenses & goals, a simple earning of salary would definitely not be sufficient at all.While everyone tries to save ‘something’ each month, it might not be an inflation beating corpus at the time of meeting each goal. We need to make that ‘something saved’ work for you, double time, which can be possible only through investments - mainly equity. At the same time, investing in multiple asset classes as part of a portfolio has proved to be efficient way to contain risk.While there are risks in certain asset classes, the volatility of returns[4][4][4][4] is reduced in a diversified portfolio of equity, debt, gold, and even real estate, while holding a certain portion in cash for investments, emergencies etc.How to go about doing it?Some basic suggestions:Income - expenditure = savings…….. Not a good idea anymoreIncome - savings = expenditure….. Saving before expenditure builds discipline, controls expenses, creates a decent, investment ready surplus.How much SHOULD I save? should not be the question….How much CAN I save? should be the thought process. This can help you accumulate a considerable surplus at the end of each month, which can be used for investing.Check if you are availing all income tax benefits[5], paying taxes on time, shunning exuberant expenditure, catering to your needs before wants. This will help you squeeze every rupee from your gross income into ‘additional cash’, which can be used for emergencies or invested wisely, consistently over a longer period of time.Ensure that you have a health insurance (family floater plan) of your own. Don’t depend on your employer’s insurance because, at any point in time, if you lose your job, you will have to start afresh and any diseases occurring during the first 2 years/pre-existing diseases might/will not be covered by the new employer’s policy. Hence, to ensure continuity of you & your family’s coverage, have your own health insurance plan.Always have a term insurance plan for self and other income generating members in your family. Take a plan with sum assured equivalent to 10X of your current gross income + existing liabilities. Incase of any unfortunate event, this amount can help the spouse/partner pay of all liabilities, while providing for a substantial corpus to support their livelihood.Nowadays, the fortunes of the companies are varying a lot and along with that, the certainty of employment. Hence, ensure that you retain an amount equal to 6–8 months of monthly expenses in either a liquid fund or a FD, as per your convenience. Nowadays, it is taking more than 8 months to get rightful employment, therefore, be prepared with a contingency fund to tide you over that period.Once you have done the basics, you can then start investing in a disciplined manner, across various asset classes.If you are a novice to financial planning, the appropriate action would begin at home, with you and your spouse sitting down and preparing notes on the consolidated financial status, liabilities, investments, surplus, insurance covers etc. Post that exercise, you can consult a reputed financial planner who can understand your situation, goals/plans before offering you a probable financial plan, to suit your requirements.The below image[6][6][6][6] is similar to putting the financial statements of any firm but much easier to put down on a paper, at a personal level.Note: Please don’t ‘consult’ free advisers or ask for plans, investment tips from strangers on public forums who don’t have any accountability to you or your wealth building plans. They are available only to make money for themselves. Also, please spend time, to understand the plan fully, to ask questions and to be prepared to continue it, without any hindrance during troubled times.There will always be iterations but agree on a financial plan and start making the necessary contributions. If you are a reader of the ‘Economic Wealth’ paper which is distributed every Monday by Economic Times, you would have already come across a financial plan and its constituents.Depending on your risk profile, financial status, cash flows, goals, investment horizon, the financial plan should be made, which at all times should reflect on where you started, how you are moving and where do you expect to reach at various points in your life.Periodic reviews are essential - You must adjust financial plans to varying inflation and returnsEquities shouldn’t be shunned as they are one of the major asset classes to beat inflation and also create a large corpus over a longer time period. Don’t fear risk, but learn/understand to accept the risk and invest accordingly. Nifty has given a 1000% return in 20 years and if we go back to Sensex for 30 years - it has given 80X returns (Sensex was at 442 points in 1987). This is not a bad return at all.No FD, RD, savings account interest could make it possible, EVER.While all the above points were for novices, seasoned investors already know what they have to do or have been doing. Incase they have been successful, then they can continue on the selected path, if not, start from scratch. Hopefully, you can still make it a success.Hope the answer is detailed enough to guide you in the right direction. As I said earlier, never take any tips / investment advice from strangers (including me).Financial data and source credits: Economic Times, Times of India, RL360, Vertex42, Trading Economics, Tradebrains images, trading chart images and other google images.Footnotes[1] Life expectancy in India goes up by 5 years in a decade - Times of India[1] Life expectancy in India goes up by 5 years in a decade - Times of India[1] Life expectancy in India goes up by 5 years in a decade - Times of India[1] Life expectancy in India goes up by 5 years in a decade - Times of India[2] Impact of Inflation on Savings Calculator[2] Impact of Inflation on Savings Calculator[2] Impact of Inflation on Savings Calculator[2] Impact of Inflation on Savings Calculator[3] Online Inflation Calculator[3] Online Inflation Calculator[3] Online Inflation Calculator[3] Online Inflation Calculator[4] How to diversify your investment portfolio[4] How to diversify your investment portfolio[4] How to diversify your investment portfolio[4] How to diversify your investment portfolio[5] 5 golden rules of financial planning[6] Financial Plan published in Economic Times Wealth on 17.07.2017[6] Financial Plan published in Economic Times Wealth on 17.07.2017[6] Financial Plan published in Economic Times Wealth on 17.07.2017[6] Financial Plan published in Economic Times Wealth on 17.07.2017

## If a number like Pi is infinite, how did people discover the numbers that are in the number itself?

I’ll give you a brief history of how people approximated [math]\pi[/math]. Some extra information wouldn’t hurt!In fact, there is a whole wikipedia page about approximations of pi if you want to read more.Early History:In the [math]3^{\text{rd}}[/math] century BCE, Archimedes narrowed the digits of [math]\pi[/math] to be between[math]\displaystyle\dfrac {223}{71}<\pi<\dfrac {22}{7}\tag{1}[/math]Using a [math]96[/math] sided polygon! And in [math]263[/math] CE, chinese mathematician Liu Hui computed [math]\pi[/math] to be between [math]3.141\,024[/math] and [math]3.142\,708[/math] by inscribing a [math]96[/math]-gon and a [math]192[/math]-gon.And not long after, Zu Chongzhi would give an even more accurate approximation to be between[math]\displaystyle 3.1415926<\pi<3.1415927\tag{2}[/math]Which wouldn’t be surprassed until almost a millennium.Middle Ages:In the [math]5^{\text{th}}[/math] century, Madhava of Sangamagrama discovered the infinite series for [math]\pi[/math] and gave a method for calculating [math]\pi[/math].[math]\displaystyle\pi=\sqrt{12}\sum\limits_{k\geq0}\dfrac {(-3)^{-k}}{3k+1}=\sqrt{12}\left(1-\dfrac 1{3\cdot3}+\dfrac 1{5\cdot3^2}-\&\text{c}\ldots\ldots\right)\tag{3}[/math]To which he calculated [math]\pi[/math] accurately to [math]11[/math] decimal places. And Persian astronomer Jamshīd al-Kāshī calculated [math]\pi[/math] to [math]17[/math] decimal places using a [math]3\times 2^{28}[/math] sided polygon!Modern-ish Era:In [math]1859[/math], G. Bauer used a hypergeometric series to come up with this [math]\pi[/math] formula[math]\displaystyle 1-5\left(\dfrac 12\right)^3+9\left(\dfrac {1\cdot3}{2\cdot4}\right)^3-13\left(\dfrac {1\cdot3\cdot5}{2\cdot4\cdot6}\right)^3+\&\text{c}\ldots\ldots=\dfrac 2\pi\tag{4}[/math]Which, although it converges moderately, can be easily calculated. (I can prove it if you want!) And in [math]1920[/math], Ramanujan gave this remarkable formula for calculating [math]\pi^{-1}[/math][math]\displaystyle\dfrac 1\pi=\dfrac {\sqrt{8}}{99^2}\sum\limits_{k\geq0}\dfrac {(4k)!}{k!^4}\dfrac {26390k+1103}{396^{4k}}\tag{5}[/math]Which computes [math]8[/math] digits of [math]\pi[/math] with each term in the series. Inspired by Ramanujan, the Chudnovsky brothers developed the Chudnovsky algorithm[math]\displaystyle\dfrac 1\pi=\dfrac {12}{640320^{3/2}}\sum\limits_{k\geq0}(-1)^k\dfrac {(6k)!}{k!^3(3k)!}\dfrac {545140134k+13591409}{640320^{3k}}\tag{6}[/math]Which was used to calculate the most digits of [math]\pi[/math].Finally, Daniel Shanks (Mathematician) found this amazing approximation for [math]\pi[/math][math]\displaystyle\pi=\dfrac 6{\sqrt{3502}}\ln(2u)+10^{\color{blue}{-82}}\tag{7}[/math]Where [math]u[/math] is the product of four quartic units. Namely[math]\displaystyle\begin{align*} & a=\frac 12(23+4\sqrt{34})\tag{7.1}\\ & b=\frac 12(19\sqrt{2}+7\sqrt{17})\tag{7.2}\\ & c=\frac 12(429+304\sqrt{2})\tag{7.3}\\ & d=\frac 12(627+442\sqrt{2})\tag{7.4}\end{align*}[/math]And[math]\displaystyle u=(a+\sqrt{a^2-1})^2(b+\sqrt{b^2-1})^2(c+\sqrt{c^2-1})^2(d+\sqrt{d^2-1})^2\tag{7.5}[/math]Note that if we make a slight modification, the formula becomes even more accurate[math]\displaystyle\pi=\dfrac 6{\sqrt{3502}}\ln(2^6 u^6+\color{brown}{24})+10^{\color{blue}{-161}}\tag{7.6}[/math]Happy pi day!

## As a girl of 22, how can I join a women's Indian cricket team?

It's great to know that few girls not only just love Cricket but they are also passionate about it. It is good that you are aspiring to represent the nation at the highest level.First of all you should focus on your cricket for at least 1 year in order to get noticeable. You should join a club or stadium.Here are some clubs/stadium in different cities where girls like you can train themselves.1. AhmedabadGujarat Cricket AssociationAddress: 230/231 Akshar Arcade, Navrangpura, Amehdabad, GujaratTelephone: +91 792 7501717Planet C4uAddress: 903 Sukh Sagar, Ashram Road, Near Fortune Hotel Asm Road, Asharam Road, Ahmedabad GujaratTelephone: +91 922 8166090Sardar Patel Stadium/Motera StadiumAddress: Near City Gold Cineman, Near Torrent Power, Motera, Ahmedabad, GujaratTelephone: +91 792 7505077Sardar Vallabnbhai Patel Stadium/Sports Club of Gujarat StadiumAddress: Navjivan, Ahmedabad, Gujarat2. BangaloreKarnataka Institue of CricketAddress: R B A N M's Choultry Ground, No. 67/68, St. John's Road, Near Commercial Street, Ulsoor Lake Shivajinagar, BangaloreTelephone: +91 802 25591089Karnataka State Cricket AssociationAddress: K.S.C.A Office, Chinnaswamy Stadium, BangaloreTelephone: +91 804 0154015Website: ksca.co.inM. Chinnaswamy StadiumAddress: Cubbon Rd, Shivaji Nagar, Bengaluru, KanatakaTelephone: +91 804 0154015National Cricket AcademyAddress: M Chinnaswamy Stadium, MG Road, Bengaluru, KarnatakaTelephone: 91 802 28689753. ChennaiJawarhal Nehru StadiumAddress: Sydenhams Rd, Periyamet, Chennai, Tamil NaduTelephone: +91 442 5368709M.A. Chidambaram StadiumAddress: No. 5, Victoria Hostel Road, Chepauk, Near Chepauk Raillway Station, ChennaiTelephone: +91 442 8514896Madras Cricket ClubAddress: 1 Bells Road, Chepauk, ChennaiTelephone: 044 – 2852397Sachin Corporate ClubAddress: 62/1 Kodambakkam High Road, T. Nagar, Chennai, Tamil NaduTelephone: 9941355158TN 11 Star Cricket ClubAddress: No. 33/16, Kavarai Street, Saidapet, ChennaiTelephone: 944478092/8144178092Web: http://www.tn11starcricket.com/4. DelhiDelhi Cricket ClubAddress: Siddharth International Public School, Near Chetak Complex, Dilshad GardenTelephone: +91 996 8910180/8800553281Delhi & District Cricket AssociationAddress: Ferozeshah Kotla Ground New DelhiTelephone: 2331932323313143, 23312721,Web: Welcome To Delhi & District Cricket AssociationDwarka Sports ComplexAddress: Sector – 11, New DelhiTelephone: 25089733Ferozeshah Kotla GroundAddress: Bahadur Shah Zafar Marg, New Delhi, DelhiTelephone: +91 993 6082777Harbax Singh StadiumAddress: Delhi Cantt, Nr Gopi Nath Bazaar, DelhiTelephone: +91 112 56945055. HyderabadHyderabad Cricket AssociationRajiv Gandhi International Cricket StadiumAddress: Uppal, Near GE Capital Complex, HyderabadTelephone: +91 402 7176873Web: Hyderabad Cricket Association: Home PageLal Bahadur Shastri Stadium Cricket GroundAddress: Abids Rd, Basheer Bagh Hyderabad, Telangana6. JaipurJaipur Cricket AssociationAddress: C/o K L Saini Statium, Kaveri Path, Madhyam Marg, Mansarovar, JaipurTelephone: +91 982 9244509Rajasthan Cricket AssociationAddress: SMS Stadium, North Pavilion, Ambedkar Circle, JaipurTelephone: +91 141 51170015117003,Web: http://crickettrajasthan.inSawai Mansingh StadiumAddress: Jan Path, Lalkothi, Jaipur, Rajasthan7. KolkataCalcutta Cricket & Football ClubAddress: 19/1, Gurusaday Road, KolkataTelephone: +91 332 4615060/5204/4656Eden GardensAddress: Kolkata, West BengalJU Arena Cricket GroundAddress: Garfa Main Rd, Jadavpur, Kolkata, West Bengal, IndiaThe Cricket Association of BengalAddress: Dr B C Roy Club House, Fort William, Eden Gardens, KolkataTelephone: +91 332 248041122483403, 22481528, 22482447,Web: http://www.cricketassociationofbengal.com/8. MumbaiBrabourne StadiumAddress: The Cricket Club of India ,Dinshaw Vacha Road,Churchgate, Mumbai, MaharashtraTelephone: +91 226 6594100Bombay GymkhanaAddress: Bombay Gymkhana Ltd., MG Road, Fort, MumbaiTelephone: +91 222 070311-12-13-149122 43223400 / 2207 08636668 /Web: http://www.bombaygymkhana.com/M.I.G. Cricket ClubAddress: M.I.G. Colony, Ramakrishna Paramahans Marg, Bandra (East), MumbaiTelephone: +91 222 640 8899/2645/7108/7109+91 222 6436594/7333/6907/7109,Web: http://www.migcricketclub.org/Mumbai Cricket AssociationAddress: Cricket Centre, Wankhede Stadium, 'D' Road, Churchgate, MumbaiTelephone: 91 002 22795500gggvhhstuuWeb: http://www.mumbaicricket.com/Wankhede StadiumAddress: D Rd, Churchgate, Mumbai, MaharashtraTelephone: +91 222 2795500Jhijjukj9. PuneMaharashtra Cricket Association StadiumAddress: Pune, Maharashtra, IndiaNehru Stadium, PuneAddress: Saras Baug, Sinhagad Rd, Swargate, Pune, Maharashtra10. SuratC.B Patel Sports ClubAddress: University Road, Vesu, Himalaya Marg, Surat, GujaratLalabhai Contractor StadiumAddress: Mahrana Pratap Marg, Dumas Rd, Piplod, Surat, GujaratSurat District AssociationAddress: Lalbhai Contractor Stadium, Vesu, Surat, Surat Dumas Road, Near Govardhan Haveli, SuratWeb: http://sdcacricket.org/You can develop your skills in these clubs/stadiums. Just follow your dreams because dreams do come true.Be dedicated,be determined who knows one day we all be watching you representing India in the cricket’s highest level.Best of luck

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