Compound Weighted Interest - Maths Puzzle

If P1 money is invested @ rate r1 and P2 is invested @r2 rate compounded annually both for the same duration, then what is the weighted avg compound rate for the total money P1+P2?

What is the weighted average rate if it were a case of simple interest? 

Solution:
Consider simple interest first of the following amounts:
300@5% and 500@7% for same duration.

Overall interest per year =3*5+5*7=50. overall Principal =300+500=800

Interest per 100 principal per year =50/8=(3*5+5*7)/8 which is the weighted avg of individual rates.

How does it work for compound interest?
Total Amount after n years

=P1*(1+r1)**n + P2*(1+r2)**n
And this should be equal to

=(P1+P2)*(1+r)**n where r is wted avg compound rate

r= [ [P1*(1+r1)**n + P2*(1+r2)**n]/ (P1+P2) ]**(1/n) - 1

In effect meaning that the weights for compound interest are the (1+r)**n factors.  Of course one has to apply the inverse root and subtract one finally

Analysis Of Financial Options - Maths Puzzle

Let's assume we have invested Rs 30 lacs in a particular debt instrument which used to give about 8% annual return. 

Now LTCG (Long term capital gains) tax on debt instruments is 20%. For the time being let's avoid the complexity of indexation. This means if a fund grew from Rs 100 to Rs 140 over a 4 year period, the gain is Rs 40. And the LTCG tax is 20% of Rs 40.

Now let's come to the problem.

I find that the debt fund returns have fallen from 8% to 6%. This means that while I used to get 8% returns till today,  the return from today to days in future wilI be 6%. I have another financial instrument which gives me the same 6% return but it does not attract any income tax - meaning the returns are tax exempt.

I am considering moving the funds from the first instrument to the second one. But if I move now, I will have to pay LTCG tax in Apr 2018. If I were to wait till Apr 1, 2018 and then make the switch, the LTCG would have happened only in the FY (Financial year) 2018-19 and the tax would have to be paid only in April 2019. We assume for the sake of simplicity that all tax is payable in April meaning the month following the end of the FY. So if I wait 4 months, I can postpone the tax by a year. 

Assume that the 2nd fund will remain tax exempt and that the return percentages will hold good for the next year or so.

Now the question:

Should I make the switch now or wait till Apr 2018?

Intermediate questions you need to answer:

1. Is the exact date that I made the original investment relevant (I assure you the date is such that the transaction will be termed Long Term).
2. Is the exact amount of original investment and the rates of return from the beginning till now relevant? Is the exact amount of LTCG till now relevant?

Assumptions:

• The LTCG tax payable on debt funds does not depend on your income. Even if you had zero income in a FY, you still have to pay the LTCG tax on debt funds that you redeemed (sold) and made a profit on in the FY.
• I do not know any IT assessor whom I can bribe. Answers pertaining to illegal methods not accepted.

Solution:

• The amount and date of original investment as well as the history of returns till now are same for both options - whether i switch right now or I switch on Apr 1, 2018. I need not hence bother with these values.
• What happens on Apr 2, 2018 or later is again not relevant since it is the same for both options.

• It is like saying you and I go on a trip.  For the 1st four days we travel together, then we split up. You go north, I go south. Then we meet up on Apr 1st 2018. Then travel together for the rest of the trip. How many more places did you visit than me? Would we start finding out how many places you saw and I saw before we split up and again after we rejoined? We need not, right? We need focus only on that portion of the trip when we were not together.

• The debt fund gives 6% but taxed @ 20%, hence nett it gives 4.8%. The other option gives 6% nett. Hence the "sell right now option" gives me 1.2% extra for 1/3 year (=4months). If the amount I have now is x, I get 1.2%*x* 1/3 more if I switch right now vis-a-vis waiting till Apr 2018 to switch.
• If y is the LTCG incurred till now in the debt fund then, if I switch now, I have to pay 20%*y as tax in Apr 2018. Remember, there is no tax on the fund I switch to. Now If I wait till Apr 2018 and then switch then my total tax will still be 20%*y (note that by using nett 4.8% as the return for the next 4 months, I have already considered tax) but I will pay the 20%*y in Apr 2019. If the cost of money is 6%, I get 20%*y*6% as interest on the tax I have deferred by a year till 2019 in case I wait till Apr 2018 to switch.
• Note that for finding out the cost of tax payment earlier I DO need to know the amount of LTCG (directly, if available, or indirectly through the amount of original investment and the avg rate or return from the date of original investment till now).
• Hence if I switch right now, I get 1.2%*x*1/3 (=30Lacs/3*1.2/100=12k) more because of higher return and 20%*y*6% less because of non-deferment of tax payment. Which is higher? Can't say.  It depends on the exact value of y. If for example y = 5Lacs, then 20%*y*6% = 6k. In such a case I should switch right now because 12 lacs > 6lacs. But if y is high enough the the expression with y will become higher then I should wait till Apr 2018 to switch. 
• If y=12Lacs, 20%*y*6% = 14.4k. In that case it may make more sense to wait until Apr 2018 to switch. This means that the 18Lacs of original investment became 30Lacs with a CG of 12Lacs. That means that the investment was held for many years so that the interest or LTCG is sizeable compared to the original principal. This also provides an instance where decision to switch to a more lucrative instrument (the second one) depends on an external forced factor of when the tax is payable - this is counter intuitive. 

Can Human Beings Recognize Others By Their Smell?

I had earlier (http://vbala99.blogspot.com/2009/09/how-does-child-recognize-his-mom.html) raised a question as to whether toddlers recognize their moms. 

A friend of mine had confirmed that they can. Couple of other friends had also told me that they can recognize the smell of their husbands and their children. This was too much. I suspected that they were taking me for a ride. So I decided to get some details.

I focused primarily on babies and their moms. And Googled. And boy did I find some interesting stuff.

Now here is the stuff that I picked up.

Babies recognize their primary care giver (PCG) and is more comfortable with faces that resemble the face of their primary caregiver. (Meaning that in those rare cases where the father is the PCG, then the baby is attracted to male faces resembling those of their father.

Babies recognize the smell of their mothers (mothers breasts apparently) and hence can differentiate, within about 3 days of birth, the smells of their mothers's vis-a-vis others' (http://www.sparkpeople.com/resource/pregnancy_articles.asp?id=742). If one of the breast is washed with soap, in order to hide the smell, the baby will avoid that breast. Quote from "Just as the baby rats would die of starvation if their mother’s scent was changed by washing her with soap, so also their mate preference can be manipulated by solely allowing them to be familiar with the scent of lemon. But this does not apply to rats alone: “After mothers apply a perfume to their breasts before nursing for a day or two, infants between one and two weeks old appear to prefer the familiar scent” (Kohl & Francoeur, 1995, p.77). While changing the mother’s scent does not cause a human baby to starve, it does change the scent that the baby prefers."https://www.inforefuge.com/science-of-smell-mother-infant-bonding 

Mothers also can recognize the smell of their babies. And these are true of humans, cats, rats (and God knows which other animals) https://thehumanevolutionblog.com/2017/11/27/cats-find-own-kittens-by-smell/. 

Research indicates that women who have been mothers recently feel differently when they smell the odor of babies (not their own) than women who never had babies. 

Quote from https://www.webmd.com/parenting/baby/news/20050706/babys-nose-knows-moms-smell: "Babies [Baby rats] learn their mother's smell early in life, wiring the scent into their brains, new research shows... {A baby] may be engraving her mother's scent in her mind, making it one of her life's earliest discoveries.

Quote from https://www.inforefuge.com/science-of-smell-mother-infant-bonding: "Pheromones also serve as identifiers. Mothers and children can recognize each other by the pheromones each emits." 

In babies, the sense of smell is much better developed than sense of hearing or of vision. The instinct (S1) and keen sense of smell that babies have is a lot like that of animals. As we grow older we develop other senses and also S2 and thus veer away from the nature of animals.

Mothers find the smell of their babies delicious. (Does not mean that moms want to eat their child. It means that the same part of the mom's brain is triggered when they smell their baby as when they see / smell appetizing food.)

I am reminded of the Thirukkural:

குழலினது யாழினிது என்பதும் மக்கள் 

மழலைச்சொல் கேளா தவர்.

meaning that only a person who hasn't heard their child speak will think that the sound from a flute or a guitar is wonderful.

Additional reading:

http://www.parenting.com/article/what-your-baby-knows-about-you

Free Will Or Paid Will?

While I have been dabbling in freewill, I came across this excellent article (https://medium.com/@darwins_apple/my-bias-about-cognitive-biases-5e0a730b651) which explains exactly how much (or little) consciousness (S2 or System 2 as against Subconscious which is S1 or System 1) is involved in deciding what we do. 

As I explained to a friend yesterday, it's like a man (S2) silly enough to claim that he takes all the major decisions at home while the wife (S1) chuckles silently in the background knowing who exactly does.

And I wonder how is it that most people I talk to won't believe this - that S2 is given too much credit.

Additional reading:

1. http://vbala99.blogspot.com/2017/10/thinking-fast-and-slow-daniel-kahnemann.html
2. Strangers to Ourselves: Discovering the Adaptive Unconscious by Timothy Wilson: https://www.amazon.in/dp/B002OEBN92/ref=dp-kindle-redirect?_encoding=UTF8&btkr=1

Forex And Percentage Problem

The FOREX value (Number of INR for 1 USD) varies as follows during a certain period:  

In the 1^st quarter of a year, it increases by d%. In the 2^nd quarter of a year, it decreases by d%. In the 3^rd quarter of a year, it increases by d%. In the 4^th quarter of a year, it decreases by d%.

It is also noted that the FOREX value decreases by 200 points in the first 2 quarters and by 192 units in the last 2 quarters of the year.

If a person had 100 USD all throughout the year, what is the overall loss percentage of the value of USD, when exchanged with INR, from the start to the end of the year?  

Solution:

There are two variables here

Let's assume exchange rate = x. d is another variable which is a fraction. for 20%, d=0.2

The rate at the end of each quarter is 

1  x*(1+d)

2  x*(1+d)(1-d)=x*(1-d^2)

3  x*(1-d^2)*(1+d)

4  x*(1-d^2)^2

Now the value decreases by 200 points meaning by Rs2 after 1st 2 quarters.

Hence x - x*(1-d^2)=2 or x*[1-(1-d^2)]=2 or x*d^2=2 ---------------(A)

The value decreases by 192 points in the last 2 quarters

Hence, x*(1-d^2)-x*(1-d^2)^2=1.92 or x*(1-d^2)*d^2=1.92   ---- (B)

Dividing B by A

1-d^2=1.92/2=0.96

d^2=0.04, d=0.2=20%

Hence x=50 = exchange rate

Initial value for 1 USD = Rs 50

Loss = 2+1.92=3.92

Loss for Rs 100 = 3.92*2=7.84 also equal to % loss.

This problem is inappropriate at school or college level because it uses the term of points which is not usually taught at that level.

What is (the amount for) Rs 1000 compounded @10% daily or hourly or by seconds for 15 days?

Solution: Rate per day is 10%/365

Amount compounded daily = 1000*(1+10%/365)^15 = 1004.117
Amount compounded hourly = 1000*(1+10%/(365*24)^(15*24) = 1004.118
Amount compounded every sec = 1000*(1+10%/(365*24*3600)^(15*24*3600) = 1004.118

If it is compounded infinitely frequently then the amount for 15 days is
A = P(1+r/(365*n))^(15*n) as n tends to infinity where P =1000 and r = 10%
=P(1+1/S)^(15*n) where  S = 365*n/r and hence tends to infinity
=P(1+1/S)^(S*r*15/365)
=(P(1+1/S)^(S))^(r*15/365) 
=e^(r*15/365) 

=1004.118

What Is Competence?

Competence in a subject is about 

• 1. the ability to handle questions or tackle issues which one has not read about or experienced in the past. 

2. The vast knowledge one has in a subject

3. The ability to find the right person(s) to solve problems or issues which one hasn't experienced or read about before

Which option do you choose. Why?

Maths Puzzle - Compound Interest Each Year

Assume principal is Rs 1000, interest is 10%. Duration is 5 years. Determine the interest paid each year.

Maths Puzzle - What Is The Rank? How Big Is The Number

Recently I got this question posed to me.

Imagine a 5 digit number (with no digit repeating and 1st digit is not zero) - example. 54312 

If you rank all the 5 digit numbers you can make with the 5 digits, how big is the number given (54312) - what is its rank?

And it has to be given as an algorithm (or formula) so that the same algorithm works for any other 5 digit number or 6 or 7 digit number.

Hmm.

With 2 digits, we can create 2! number of 2 digit numbers. For example with 3,5

we can create 35, 53. With 3 digits, 3,5,8 we can have 3 as the 1st digit and create 2! numbers with the other digits 5,8. We can create 2! more numbers with 5 as the first digit and 3,8 as the other two digits. And one more set of 2! numbers having 8 as the 1st digit and 3,5 as the other two digits. Hence 3*2! =3! is the total number of numbers possible with 3 digits (none repeating and no zeros - just to keep it simple).

With 4 digits, the answer is 4! and with 5 digits it is 5!. Obviously this algorithm will work only up to 9 digits since no digit can repeat and zero isn't allowed.

Now to find out the rank of a given 5 digit number (either we need to find the number of numbers bigger than the given number or smaller than the given number). Let's say we find the number of number bigger than the given number.

Let's take the number 34512

Take the 1st digit (from Left) = 3

How many digits can be higher than this digit 3? 4 and 5. Two digits can be bigger. With each digit in the leftmost place, we can have 4! numbers with different combinations of digits from 2nd to 5th digits from L to R. So a total of 4!*2 (2 standing for 4,5 the two digits bigger than 3) numbers are possible based only on the leftmost digit. 

Now come to the 2nd digit 4. How many digits are bigger than 4? Only 5. Freezing 35 as the first two digits, how many numbers can be formed with the other three digits? 3!*1 (one standing for 5, the only digit than is bigger than 4)

Now we come to the 3rd digit 5. 5 is the biggest number. Hence we cant any bigger number coming from the 3 digit.

4th digit 1.

How many digits are bigger than 1? Only 2. The last two digits can be 12 or 21. Only one number is possible.

Now adding all the numbers bigger than the given number, we have 4!*2+3!*1+2!*0+1=48+6+0+1=55.

Look at the digits and rank sheet in the file: https://docs.google.com/spreadsheets/d/19aRJBpZz8O2TY1nbMsSoTm2RycN3SqT9qH_s1VZlCYs/edit#gid=612883050. The number is 65th in rank with 55 more numbers bigger. We got 55 numbers bigger. We were right.

So the logic is:

take the 1st digit (leftmost): find how many digits are bigger than the one we have. Multiply that number by (n-1)!. 

Repeat this with the 2nd digit and 3rd digit and so on. When you come to the last 2 digits, there are only two numbers possible. Either ours is the biggest or there is another number which is bigger. Add up all the numbers. That provides the rank.

Incidentally, the number of possible combinations of 5 digits is 5! = 120.

Maths Puzzle - Digits, Dates, Clock

What is the last digit in 

• 11**11
• 4**65
• 6**15
• 7**23
• 18**23
• 19*101
• Which is bigger 9**25 or 25**9

And clocks:

• At what time between 4PM and 5PM are the minute and hour hands together?
• At what time between 3PM and 4PM are the two hands 15 deg from each other

Start with 12 O Clock position as the zero degree. At x minutes past 4PM what are the positions of the hour hand and minute hands in degrees from 12 O Clock?

Calendar: https://docs.google.com/spreadsheets/d/19aRJBpZz8O2TY1nbMsSoTm2RycN3SqT9qH_s1VZlCYs/edit#gid=612883050 .
(the file has one error. February is hard coded to have 28 days.. It doesn't consider leap years. To that extent the day of the week calculated will be off by 1 day for dates in a leap year after the month of Feb)

What day of the week was

• Jan 29, 1934
• Feb 1, 2217
• Oct 2, 833

Solution tip:

• Every year (normal one) has 52 week + 1 odd day. (I came across this terminology in a maths book) and am using the same terminology here.
• Every leap year has 52 weeks + 2 odd  days
• Every 4 years has 3 normal years + 1 leap year and hence 3*1+1*2=5 odd days total. so if today (Nov 21, 2017) is a Tue, then the day 4 years later Nov 21, 2021 has 5 odd days and hence 5 days after Tue. Count  Wed=1 odd day, Thu=2, Fri=3, Sat=4, Sun=5. Hence that day is a Sunday
• Every 100 years has 24 leap years and 76 normal years because the century year like 2100, 2200 are not leap years. But century years such as 2000, 1200, 400, 3200 etc are leap years. Don't ask me why. That's how it is. Hence 100 years have 24*2+76*1=124 days = 17 weeks and 5 days. Removing the exact number of weeks, the odd days in every 100 years = 5.
• Every 400 years, number of odd days = 3*5+1*6=21 = 3 weeks exactly. Hence odd days = zero. 400 years has three numbers of hundred years (which are not leap years) and one number of 400 years (which is a leap year)
• Let's take Nov 21, 2017. We count the following to arrive at this date
• 400*5=2000 years
• 4*4=16 years
• 1*0=0 years
• 10 months (Jan to Oct of a non leap year)
• 21 days
• Now, 
• 5 sets of 400 years give 5*0=0 odd days 
• There are no sets of 100 years - so 0 odd days
• 4 sets of 4 years give 4*5=20 odd days
• There are no sets of 1 years - so 0 odd days
• Jan till Oct: 365 - (31+30) =304. I subtracted Dec and Nov days from 365 which is easier than counting all days from Jan to Oct. 304 days gives 43 weeks and 3 odd days
• 21 days in Nov=3 weeks and 0 odd days
• Counting only odd days: 0+0+20+0+3+0=23 = 3 weeks and 2 odd days = 2 odd days. 
• Now the final step is this: take the number from the previous step which is two in this case. If zero then Sun, if one then Mon, if two then Tue and so on. Hence Nov 21, 2017 is a Tue.

What is the date 121 Tuesdays before Oct 29, 1965?

Where You Might Want A Retirement Home

A friend and I were discussing and the thought of a retirement home came up.

First, why do we need such a place? Because old age homes may not be good enough in terms of care provided or maybe too expensive. Children may not live with parents. Parents (old) may not be able to live all alone. And hence this thought.

We tried to specify what might be needed in such a place. 

Since everyone would be old having arthritis, diabetes etc the place had to have medical facilities and ambulance should be available within 30 minutes and a good hospital should be available within an hour's drive. Of course other amenities like continuous availability of good water, electricity and Internet are also expected in that place.

For those who do not reside in India, this may come as a shock since these are expected to be present anywhere. Well these are present in major cities but may not be in interior India.

If 4 families were to get together - the idea being that they are available, in case of emergency, for each other, they could pool in and buy 1 ground (2400 sq ft) and construct small apartments for each.

Cost of construction being about Rs 2500/sq ft now, a small 1BHK 600 ft would perhaps cost about Rs 1,500,000. If there was a good location away from the metropolis but still within an hour distance from hospitals, 1 ground might cost Rs 50 lacs. Split 4 ways, the land cost might about Rs 1,500,000 including registration and other charges. Note that this is only the land cost. The construction cost of 2 flats in 1st floor (with ground floor for car parking) and 2 flats in 2nd floor would be about 1,500,000 per family as explained earlier. 

The total cost per family would be Rs 3,000,000 (about $50,000). And for that price each gets a small 1BHK apartment and equal share of a 2400 sq ft property (undivided share of 600 sq ft). Of course this does not include the cost of special interiors or of car etc.

One could just buy the land initially and postpone construction of the flats. Land price generally rises much much faster than construction cost. So this might be hedge against rising prices. Flats can be constructed at a later date when the families need to move to that place. All the families may have a home right now and have members working in the city. 


Would we be willing to spend Rs 3,000,000 for such a flat? And of course you have to manage your own maintenance, ensure that Metro (corporation) Water is available etc. What other environmental factors would we look for in such a flat?

1. As mentioned earlier - Hospital, ambulance, water, electricity, Internet etc.
2. Place being safe even at night. Proximity to local transport. 
3. There is no particular danger of flooding or other natural calamities.
4. That the property has all the necessary approvals from other government agencies. This would help apply for bank loans.
5. The plot is of a reasonable size that it will find buyer(s) when the decision is made to sell. 
6. That there is no fear of encroachment during the time the plot is vacant or when flats are unoccupied. 
7. That the people in the neighborhood are not hostile towards the communities to which the 4 families might belong.

Related to the above are other points with respect to dissolution (or dilution) of the 4 family units or other intrafamily issues which are listed below:

• Note that one or more of the 4 families might want to opt out at any time. Would there be buyers to buy one plot in a "society with only 4 flats". 
• What would the mechanics be when the 4 families consist of 3 members from the original four and a new family? Would this cause an issue?
• Considering that the flats will be in 1st and 2nd floor, how would we entice 2 families consider the 2nd floor should everyone want the 1st floor flat? Or, the other way around if the 2nd floor were to be more appealing than the 1st floor for any reason.
• Design and maintenance of common utilities such as:
• Garden, if any
• Sump
• Water purchase in summer and draining during monsoon

You Scratch My Mat, I Scratch Your Back

A friend of mine F told me about an incident that happened around midnight a few days back. She has a daughter D and a husband H. Apologies to F for reproducing the story without her permission.

F had forgotten to switch off the AC one night. And it had become very cold. D (daughter) woke up shivering. But D didn't wake up F nor did she use the remote to switch the A/C off. I asked F whether D knew how to operate the remote. Maybe D was like me. F assured me that D knew the use of remote inside out. 

Going on further with the story, D was scratching the mat and F woke up from the sound and found D sitting and staring at her. F asked D "why are you up?". D replied that she was cold and a/c blah blah. F asked D angrily "why didn't you wake me up or use the remote? Are you an idiot?" D meekly replied that she didn't want to wake mother up and disturb. H woke up in this melee and asked the two of them what was going on. F explained to her husband. H said "Wow, D is so sweet" and then they all slept happily ever after (after switching off the A/C).

Small incident. It was not as though North Korea had fired a nuclear missile to destroy Moscow (making it seem as though the Americans did it etc). I am pretty sure CNN would not consider this as breaking news.

Now let us, like Mandira Bedi and Sindhu, do some behind the scenes analysis.

• Why did D not use the remote?
• Why did she scratch the mat and make a noise - F (friend) told me it was to wake the mother up.

D wanted a small emotional drama at the dead of the night. The cost involved was putting up with 3 minutes of extra cold. And the pain in nails scratching until mom woke up. Now did D use S1 or was it S2's decision? I am not sure yet.

If D had used the remote, the problem would have been solved but with no drama. Now in life do we need more drama or do we want to switch off A/C fast? Which would give more bonus points to D (father's approval at the end)? 

Another incident came to my notice which is similar and provided a perspective. A friend has an attendant who is very very reliable. Now this attendant had to attend a marriage of a friend and had informed my friend's family of the date and that she would have to be away, a month in advance. And that a new attendant would come as a replacement.
As luck would have it, my friend was diagnosed with some issue and had to undergo surgery the date of which overlapped with the attendant's leave.

My friend kept mentioning to me that it was an unfortunate complication that the surgery and the attendant's leave was happening at the same time. I asked my friend whether she wanted the attendant to cancel or postpone the leave and forego attending the marriage. My friend said no, that's not what she had in mind. She was just mentioning. Couldn't she even say what was troubling her..

Now in the case of my friend's daughter D and the the A/C incident, if someone had asked D whether she was scratching the mat in order to wake up her mom and have the A/C switched off, her answer would have been no. Would D have continued scratching the mat if her mom was awake or if the A/c was off? Obviously No.
Would my friend who had a surgery complained if her attendant was not going on leave, no again. But was she complaining in order to get the attendant to cancel or postpone the leave? My friend says no.

Are my friend with surgery and the friend's daughter with A/c unaware that their actions (complaining about leave or scratching the mat) had a specific purpose? And that their actions would stop once the issue was resolved? 

To me it seems so obvious but to them their acts were just a way of expressing their discomfort but with no direct purpose in mind.

Expressing a discomfort without mentioning a solution involves a position that one isn't demanding. That one was just expressing discomfort. If the audience is smart, they would address the issue. If the audience doesn't get it and hence the issue remains unresolved then there is still the advantage of not being seen as demanding. It's not even about being demanding. It's about expressing a need.

I guess some people strongly prefer to be seen as not being needy. They express their needs often. They do it in an oblique way. Perhaps in the hope that at least some of their needs would be addressed. And without being seen as needy.

Wow.


Additional reading:

1. http://vbala99.blogspot.com/2017/06/relation-between-nt-sf-natural.html
2. http://vbala99.blogspot.com/2017/10/s1-and-s2-daniel-kahnemann-my-examples.html

The Best Performing MFs In India

I had earlier (http://vbala99.blogspot.com/2017/07/second-time-investors-in-mutual-funds-mf.html) written about second time investors. Recently a friend asked me to recommend some mutual funds.

While I was browsing yesterday I happened to come across an article in one of the business sites which listed the best mutual funds and their returns over 3, 5, 10 periods for equity funds and over 3 month, 6 month and 1 year period for debt funds. 

Obviously whoever created the data had not presented the data in a spreadsheet friendly format. I got the data and ported the same into a spreadsheet and did some cleaning of the formats. 

Here is the spreadsheet: https://docs.google.com/spreadsheets/d/1sEifwbil4YVtqsR7wls1W6y2xj9YoP9EYA_m6p9zh_Y/edit?usp=sharing

This data is for India MFs as on the date this post was written and I have taken the data from a business magazine. No data has been changed. The columns in red font were added by me. And I have sorted the column "Weighted Annual Return %" descending. So that the best funds are listed on the top. I have not differentiated the fund types (a debt fund, an ELSS fund and a midcap fund are all put in the same basket). The type of fund is mentioned in the first column. You can filter, sort do whatever. For some equity funds 10 year data is not available and the last column is "N". If you are rather particular about funds which have been around for 10 years or more then filter for the last column = Y.

Have fun.

Additional reading:

1. Historical BSE data: https://in.finance.yahoo.com/quote/%5EBSESN/history?period1=1418322600&period2=1513017000&interval=1mo&filter=history&frequency=1mo
2. Mutual funds for which Karby is registrar: https://www.karvymfs.com/karvy/InvestorServices/InvCustomerCare.aspx