ECONOMICS:

[Azured]

INTRODUCTION:

as i promised here is my second guide, admittedly its not a tech guide but i believe all of us have to know about it as it brushes on every single persons life, Economics, in many ways it controls our life, many of us have loans, mortgages, saving accounts and bonds or investment accounts yet most don't know the basic calculations that will roughly protect you from being cheated off or into certain investments, loans or saving plans. so here i am, this guide will provide you with an easy way to find out what is best for you.

Using compound interest tables (these are readily available all over the web but will also be provided here) i will give examples on cases organized in an ascending order of difficulty.

first off i'll describe my approach on the issue, this part is really important if you wish to fully understand the concepts, naturally i will post pictures and use graphical approaches wherever its possible. I will also color code every section so it will be easier for each person to find and read the section that addresses their problems directly.

in this first guide (yes i will make a follow up asap) 6 cases will be introduced, these are the most common, there are more of course and combination's as well, i will try to present them all as i plan on making 3~5 guides regarding these issues to cover most aspects of life, each guide will be more case oriented and specific in nature, as for this one as i said i will explain six aspects.

PS: personal inquiries are welcome and i will try to help as much as possible with case examples.

PSS: i am not an economist nor do i specialize in any field of business or accounting, i am a civil engineer and most of the information provided here is based on my understanding of Engineering Economics (even though its called Engineering Economics it is in fact the way everything operates from and based upon) such as it is, anyone with an economic background is most welcome to review this thread and later ones to advice, criticize and correct anything they find wrong or questionable.

BASIC CONCEPTS:

there are two basic actions of importance the first is "Borrowing money" and the second is "Giving money/Investing", things that are also quite commonly found are "Interest" both for borrowing and investing -will be indicated using the letter "i" (i.e 10% interest means that i=0.10)- and the number of years related to the financial decision (i.e life of the loan or investment) -will be denoted by the letter "t"- . these two letters are commonly used in most books that discuss this matter. For the two actions described earlier its important to know how i will represent them graphically, usually being able to break down a financial problem graphically greatly reduces the difficulty of the problem, however this should be done very carefully, as a misinterpretation can have dire effects on the results you get. The following diagrams illustrate my presentation.

1: Finding a future value based on current investment or a set portion of money (eg. if i invest 1000$ what will be the return 5 years from now).

2: Finding the current amount of money needed in order to secure a future value (eh. if i want 10000$ as a return 5 years from now how much must i invest).

3: Finding the value of payments made against a loan (eg. if i borrow 10000$ from a bank how much do i need to pay per month if i wish to repay it in 5 years).

4: Finding the amount actually borrowed when you have to pay a sum of money in installments. (eg. you are paying 1000$ a year how much is the total now).

5: Finding the installments needed to achieve a return future value. (eg. similar to a retirement plan, 401k etc..., if i save 10000$ yearly when i retire how much will i have).

6: Finding the future value of current savings. (eg. how much will be the return on you current retirement plan).

Note: the values you get are optimized and real values might differ slightly.

Figure 1:

this figure with an arrow up will indicate borrowing money from a bank, anything similar i.e involving the borrowing of money or gaining income will also be indicated with an arrow up.

Figure 2:

conversely an image with an arrow down will be used to show the spending off or investment of money.

Note: the spaces between the arrows indicate a period, this period depends on the distribution of interest, it maybe annually, semi annually (every 6 months), quarterly (every 3 months) etc...

1: Finding a future value based on current investment or a set portion of money

F = P (1 + i/n)^(nt)

where

F = future value

P = initial deposit

i = interest rate (expressed as a fraction: eg. 0.06)

n = # of times per year interest is compounded

t = number of years invested

this equation fits the simplest case scenario, you have a certain sum of money that you wish to put in a savings account that pays i interest compounded n times a year for t years, the following is a numerical example.

eg.

suppose you have 1000$ that you kept in an account that pays 6% interest compounded semi annually for say 5 years, what will the balance be after the passing of 5 years?

putting the numbers in the equation we get, 1,343.92$.

this same value can be found in a much more easier manner using the compound interest tables and will be demonstrated in the next example.

1-1: Simplified Compound Interest Equation

When interest is only compounded once per year (t=1), the equation simplifies to:

F = P (1 + r)^T

where r = i/n and T= nt but since n=1 (once a year) r=i and T=t.

1-2: Simplified Compound Interest Tables

an even easier way to solve the previous problem is to use the tables (provided at the end of the post), if we go to the table of i= 3% (the interest is compounded semi annually hence the interest 6% per year is divided by 2) then scroll down the very first column (Single Payment - Compound Amount Factor F/P) to 10 (2 payments a year for 5 years) you will find a value of 1.344, this value is multiplied by the original 1000$ to get 1344$ which is identical to the result of our previous example, this makes sense since both have exact conditions.

one might argue that using the equation is much more straight forward, in this particular case i agree, however things are not as easy as this example, in real life we have to deal with much more complex situations as such different cases arise and i will tackle them to the best of my abilities.

2: Finding the current amount of money needed in order to secure a future value

this method is the most used one by head planners, back in Syria the government has a saving plan that pays 8% interest for Syrians, as such people think of saving say 1000000 Syrian pounds, they use this equation in order to find out how much the initial value must be, this equation is non other that the previous one except the order of unknowns is changed making F known and P unknown.

from here on i will explain the steps associated with the use of the included tables for simplicity.

eg.

suppose you want to have 100000$ at the end of a 5 years investment, the financial institution that you will invest it gives a 6% interest per year compounded yearly how much must you invest ?

from the second column (Single Payment - Present Worth Factor P/F) in the i= 6% you and year 5 you will get a value of 0.7473 multiply that value by the 100000$ that you want and you get 74730$ this is the amount you need to invest now in order to get 100000$ after 5 years.

3: Finding the value of payments made against a loan

ok now things get a bit more complicated, we all (most of us at least) take car loans, personal loans etc.... , if we know the interest rate that we are repaying we can set up our own plan to repay the loan, say you take a low interest loan for 5 years, but you have the ability to pay more than the required installments, it is possible to calculate a value to repay banks in say 3 years that way you can enjoy the low interest rate without the long period (low interest would actually cost you more in some cases depending on the period).

eg.

i borrowed 10000$ in a car loan to be re-payed over the course of 4 years with an interest rate of 5%, how much must i pay each year ?

going to the table of i= 5%, then third column (Uniform Payment Series - Capital Recovery Factor A/P) at year 4, we get the factor 0.2820 we multiply it by the 10000$ borrowed to get our yearly rate for each of the 4 years, suppose you have the ability to pay in 2 years instead of 4 scrolling up the same table to year 2 we get the factor 0.5378, each year totaling 10756$ now comparing it to the 4 year plan which totals to 11280$ you find that by paying it earlier you end up paying less interest, this is actually useful and i have personally done it, i took a 6 year loan on my car at a rate of 4.69% but paid a little more on every payment so that i can be cleared in 4 years instead of 6 it saved me quite a good sum of money.

4: Finding the amount actually borrowed when you have to pay a sum of money in installments.

ok this isn't exactly very common, as i doubt anyone would come across this situation, the only scenario where this comes to mind is buying a used car where the the installments have yet to be finished and the buyer only pays what is left of the installments, the technique described here will help the new owner find out for how much the original owner bought the car for. if they are that curious.

anyways the approach for this case is just like the previous case, the only difference is that you will multiply the factor you get from the interest table, fourth column (Uniform Payment Series - Present Worth Factor P/A) then the year with the amount you are paying every installment to get the present worth, i will not give an example on this unless i get a request for one since i find it a very rare case.

5: Finding the installments needed to achieve a return future value.

now in this section and the following one things get really interesting, we all have plans for our retirement don't we ? how would you like to have 1000000$ by the time you retire? iis it possible? well yes it is very much possible, if you have a good trust fund or retirement plan, in this section you will learn how to calculate the amount you need to save each year in order to achieve your goal i will illustrate it in the following example.

eg.

lets say i want to have 1000000$ by the time i retire at the age of 65, i am 22 years old now that leaves me roughly 45 years in which i can make this possible, my savings plan gives an 8% interest a year if i go to the table with 8% interest, fifth column (Uniform Payment Series - Sinking Fund Factor A/F) then scroll down to 45, i get the factor of 0.00259 multiplying it with 1000000$ i get a value of 2590$ each year, sounds insane doesn't it?

but it is very much true, but don't start jumping for joy yet as with time money loses value (roughly 25% each 10 years) so 45 years from now a million dollars might not seem that much money. (an example is 45 years back a millionaire had the same social status as a billionaire these days).

6: Finding the future value of current savings.

this is the other part that concerns us, most of us already have their savings plans rolling, its important to know how much will they yield at retirement, again using our tables (eternally grateful for) and go to the table with the required interest, sixth column (Uniform Payment Series - Compound Amount Factor F/A) then the years you have bean saving and planning to carry on your savings till retirement, we get the factor and multiply it with the amount we are saving. to find out how much we get.

eg.

reversing the previous example lets see at year 45, i= 8% and yearly savings of 2590$ we have the factor of 386.5 doing the math we get the result of 1001035$ which roughly compares to the 1000000$ we got before.

CLOSURE

in the end of part one of the guide its important to mention a couple of things, first off i am eternally grateful to my Engineering Economics Professor for prepping me up to be able to tackle these life issues, thanks also go to the people who gave me the drive to make this second guide namely everyone who commented on my first guide, and everyone in this forum generally speaking of course :p .

1: these calculations do not take into account taxes unless they are included within basic economy (in UAE, Syria and many other countries taxes are included in the price or fee of a service hence no need to calculate it separately).

2: the last two columns will be discussed in later guides.

3: combination of the previous basic example will also be addressed in future guides.

4: the tables used in these guides can be found here and here.

this was damn tiring.........

Edited July 24, 2008 by Azured

[MackTK]

(Y) GREAT job man, you practically summarized my first finance course in college

[Azured]

glad to hear that :D, if this summarized your first course then i have achieved an unplanned goal, i'm making the second guide now, if you need it i can scan my notes and send them to you, although i'm not sure how useful they might be to you but it never hurts to check things out.

hope you find the rest of my upcoming guides just as useful.