Financial Mathematics:Magical Numbers 72,114 and 144

It is always a tedious job to calculate rate of return on various products to take investment decisions.

In financial mathematics there are certain magical numbers which would help you in calculating the rate of return for doubling,tripling or quadrupling or if rate of return is available it can help you to calculate time required to double, triple or quadruple your capital

Let us find out how :

Take an example of Mr.Doguna who has been advised by one of his agent that there is an investment opportunity whereby he can double his money in 8 years. Now Mr.Doguna wishes to calculate the rate of return of the same. 

What he need to do is just divide 72 by the no. of years. i.e. 72/8 = 9%. 

So the approximate rate of return would be 9%.Although it doesn't give an exact result but you can have a rough calculation by doing this.

Lets say Mr.Doguna got an rate of interest of 12% and now he wishes to calculate the time period required to double his amount then he need to divide 72 by rate of interest i.e.

72/12 = 6 years (approx.)

Similarly you can calculate period/rate to triple your money by dividing 114 by the available variable and to quadruple replace magical no.114 by 144. 

for example if you wish to triple your money in 12 years required rate of interest would be 114/12= 9.50%.

To quadruple your money in 16 years required rate of return would be 144/16 = 9%.

In above example if rate of return is available and you wish to calculate time period divide magical nos. by rate of return.

Hope, above nos, will help you to make certain calculations on your fingertip without depending on software, excel sheet or financial calculators to take informed decisions.

Financial Mathematics - "Itni Shiddat se maine tujhe pane ki koshish ki hai, ki har zarre ne mujhe tumse milane ki saazish ki hai".

Very rightly said that "Journey of thousand miles starts with a single step".Same way to achieve big goals in life the first step is to start with basic i.e.decide your goals/dreams or aspirations in life.

Just list down whatever you think without thinking ki "Yeh kaha se hoga". (Had we ever thought that people would be booking tickets to travel mars).

Many a times investor tells me it doesn't make sense to plan, as I don't have any surplus funds. I ask them forget what you have atleast make a list of goals you want to achieve and as soon as you make that list and refer it on regular basis, your goals themselves finds way for required investment.

You will automatically cut down on discretionary or unnecessary expenses. It will act as an alarm "That if you buy the things which you don't need today, may be tomorrow you will not be able to buy the things you need". It will motivate you to work more efficiently to grow in your career or business.For sure, the passion and better planning will make you reach your goals Like SRK says "Itni Shiddat se maine tujhe pane ki koshish ki hai, ki har zarre ne mujhe tumse milane ki saazish ki hai".

After first step of deciding goals, it requires you to put time left and amount required for it.

Today we will learn how to inflate present goals cost to future value, so that we don't end up receiving the value which do not meet the requirement as briefed in my earlier blog:http://www.rajtalati-abminvestment.blogspot.in/2014/01/calculating-rate-of-returns-before.html#links. 

In addition to that we will also learn how to calculate annual investment required to reach that value :

Let's take an example of Mr.Sapnelal who wish to plan for marriage of her daughter Ms.Dreamgirl 18 year hence. Present exps. according to kind of wedding he wish to plan for is Rs.800000.00. He expects inflation during this period will be around 7%.

First of all open an excel sheet and go on "insert" select "Function" and in "window search for function" type "FV".Following window will open :

Inputs:

Rate - It is the rate of return/inflation considered in our case it would be 7%

NPER is no. of period - In our case it is 18 years.

PMT Payment - It asks for Periodic payments you wish to make for the goal. As we want to learn how to calculate Periodic payment in next step we will keep this as blank.

PV - This is the present value of goal in our case it is Rs.800000.00.As it shows investment (Money going from our pocket) a  -ve sign to put in front of it.

Let's insert the data in above field. The result will reflect at the bottom (above the Blue highlighted line Help on this function") under Formula result as follows :

The amount required after 18 years would be Rs.2703945.82.

Now,let's see how to calculate annual amount required to be invested or periodic investment required to achieve goal of Ms. Dreamgirl's marriage.

Mr.Sapnelal risk profile is aggressive and as the period of investment is also longer he wishes to make this entire annual contribution to equity and he expects equity to give him atleast 15% return on his investment.

So. let's calculate the per annum amount required to be invested.

First of all open an excel sheet and go on "insert" select "Function" and in "window search for function" type "PMT".Following window will open :

As detailed above put the data in fileds as follows :

Rate - As Sapnelal wishes to invest the amount in equity and expects to get a return of 15%. Enter 15% against Rate.

NPER - Enter 18 as maturity is required after 18 years for Dreamgirl's marriage

PV - Enter the lumpsum amount if you wish to invest initially together with the annual amount. In our case its nil so will keep it blank.

FV - From the first calculation we got this amount which we want to achieve i.e. 2703945.82.

Type - If you wish to make contribution at start of the year then put 1 and in case of end put 0.In our case it at the beginning of the year so enter 1.

After inserting all the above details result i.e. annual requirement will reflect as follows :

So the required amount is Rs.31004.35 it is showing as negative because it is going out of our pocket or we need to make this investment.

The best part is just by changing the figures in rate you can see the value of annual investment required. If you wish to achieve your goal by investing in a bank FD and expects to get a return of 9%. Your annual investment required will become Rs.60063..04.

So plan your investment in better way irrespective of what your name means- So being Mr.Sapnelal, enjoy marriage of daughter Dreamgirl the way it was planned.

Financial Mathematics -Calculating rate of returns before investment - Let's learn how

It's a common practice in financial industry that products are sold by projecting maturity value. Reason is human mind always looks at maturity value in today's term, but forget to measure impact of inflation and rise in expenses due to standard of living. We just get obsessed with the higher absolute value and forget the actual return it generates. Instead of focusing on maturity value if we start concentrating on returns we can take much better decision. Illustrating how just looking at maturity value can make our plans a haywire and that too when we actually in need of it.

One of my friend Vivek bought an Life Insurance policy for his son's education in the year 1999 for an 18 year term on becoming a proud father. The TOTAL cost for a good engineering course was almost Rs.40000 at that time.Let me remind you during late 90's a person at senior executive level used to get salary in range of Rs.20000 to 40000 pm. Household exps. for a family of 4 for an average middle class person was in the range of Rs.4000 to Rs.5000 pm. 

With an intention that his son should not compromise during his engineering studies he planned for an maturity of Rs.1 Lac, for which was required to pay premium of Rs.3000 equal to his one month Exp. or 75% of his monthly salary.

Inspite of planning for double the amount required. When his son will reach in STD 12th i.e in the year 2017, I doubt whether he would be able to pay even the tuition and entrance examination fees for engineering courses with maturity of above policy.

Biggest reason was he thought everything in 1999's context and he thought by paying Rs.3000 which was a big amount for him at that point in time he has secured his child's education.  As against that if he would have calculated the returns he might have understood its meager 7% per annum.

Let's learn how to calculate returns so that we do not face such problems.

Open an excel sheet and go on "Insert" select 'Function' under category select "Financial" and in window search for function type "Rate". The following box will appear after clicking OK.

Inputs ;

NPER is no. of period - In Vivek's case NPER is 18 years i.e tenure of payment. In case frequency of payment is Monthly multiply it by 12,in case of Quarterly by 4 and for Half yearly by 2.

PMT Payment - periodic payments or regular payment e.g Insurance Premium, EMI Installment, Monthly Post recurring Amt. etc.In case of an FD (Its Only 1 time Payment) so leave this filed blank.
In case of Vivek it is Rs.-3000.00. In case we are making payment that should be shown as (-) and receiving money should be shown as (+) or nothing.

PV - This field should be used in case of single or one time payment like for FD,Bonds, MF investment etc.In our case as it is periodic investment we will keep it blank.

FV - This is the desired corpus or the maturity amount product offers or required.As funds are flowing in we need not put any sign before it. 

Type - Applicable only in case of periodic or regular payment. In case you are paying in advance then you should put 1 and in case of end put 0.In our example it is 1 as we pay premium in advance.

Guess - It is not visible in above picture but in excel sheet when you will scroll down you will find it, no need to put anything in it. But in case any error comes then you should put approx. return which you think it would give. Most of the time you do not require to provide anything in this field.

Let's put above data and find the result which would be as follows :

You can see the Formula result as 7% at the bottom. In case frequency is taken as Half Yearly you need to multiply result with 2, for Quarterly by 4 and in case of Monthly by 12.

In this way you can calculate Interest on EMI and returns on FD, SIP, Insurance Policy etc...

While planning do not forget to consider effect of inflation and rise in exps. due to standard of leaving.

Great Investment opportunity for lower tax bracket or no tax individuals

Great news specially for senior citizens who are facing really hard time with their retirement funds because of high CPI inflation of almost 10%/Yr. for last 3 years and low interest rates.

RBI has atlast launched the much awaited Inflation Indexed National Savings Securities - Cumulative (IINSS-C) as promised. It is in continuation of Inflation indexed bonds (IIB) launched earlier. 

IIB's were targeted at large investors, so the markup- the additional payment over and above the inflation rate or the real coupon (interest) was arrived at via competitive bidding. RBI plans to pay this real Coupon on regular basis, then inflation component will be added to the principal and paid only at the time of redemption.

In a way it offers twin benefit first it protects the principal from inflation and you get the real value at maturity and second is an increase in cash inflow every year even when the real coupon rate remain constant.e.g. If Rs.1 Lakh invested in IIB and real coupon raet is 1.5% and the Whole sale price Inflation for 1st year is 5% then real payour for first year would be Rs.1500(1.5% of Rs.1 Lakh) and that for the 2nd year will be Rs.1575(1.5% of 1.05 Lakh).

But as the IIB were linked with WPI (Wholesale Price Index) it could not interest retail investors. As historically investors are more affected by CPI (Consumer Price Index) which is much above WPI. Like WPI for November was 7.52% whereas CPI was 11.24% i.e. a difference of 3.72%.

Now RBI has realised the same in the benefit of retail investors and has come up with IINSS-C (Inflation Indexed National Savings Securities - Cumulative) which is linked with combined CPI .Rbi has also avoided competitive bidding and markup fixed of 1.5% over CPI.

Obviously it is going to be a great instrument for the people who are in lower tax bracket or with non taxable income. I think they are the one who needs real protection from falling interest rates and rising inflation.

Appending below the scenario and benefits to investors :

IINSS-C Returns for difference tax Bracket Considering markup of 1.5% on base rate Tax Slab NIL Inflation Rate 8.00% 9% 10% Interest Rate 9.50% 10.50% 11.50% Effective Rate 8.00% 9.00% 10.00% Effective Rate due to half yly compounding 9.73% 10.78% 11.83% Tax Slab 10.30% Inflation Rate 8.00% 9% 10% Interest Rate 9.50% 10.50% 11.50% Effective Rate due to half yly compounding 8.73% 9.67% 10.61% Tax Slab 20.60% Inflation Rate 8.00% 9% 10% Interest Rate 9.50% 10.50% 11.50% Effective Rate 7.73% 8.56% 9.39% Tax Slab 30.90% Inflation Rate 8.00% 9% 10% Interest Rate 9.50% 10.50% 11.50% Effective Rate 6.72% 7.45% 8.17%

Now lets look at negative side - Interest is accrued and compounded every six months. Hence even though you do not receive interest tax has to be paid in each financial year.Looking at above calculation the IINSS will still not be that attractive for retail investors in higher tax bracket and also for senior citizen who requires regular income should avoid IINSS-C.

Instead of that it is better to invest in Tax free bonds, although it doesn't carry guarantee of Central bank.But with good credit rated bonds you have much better returns net of tax annually with much lower risk.