Lesson BASIC FORMULAS AND ASSUMPTIONS USED IN FINANCIAL FORMULAS

Source code of 'BASIC FORMULAS AND ASSUMPTIONS USED IN FINANCIAL FORMULAS'

This Lesson (BASIC FORMULAS AND ASSUMPTIONS USED IN FINANCIAL FORMULAS) was created by by Theo(13342)

GENERAL INFORMATION

The terminology used below is mine.  It is fairly consistent with standard terminology, but you will find other formula presentations may use different words to mean the same thing.

Some might use Investment or Amount or Capital for what I refer to as Present Amount.
Others might use Annuity (ANN) for what I refer to as Payment (PMT).
The formulas are the same regardless of the terminology used.

I use Interest Percent, or Percent Interest to distinguish between percent and rate.  Others might refer to the Percent Interest as a rate.  The key here is that Percent needs to be converted to the decimal equivalent in order to be used in these formulas.  If you see something like interest rate = 10%, you need to convert the percent to it�s decimal equivalent which would be x%/100% which winds up being x/100.  If 10%, then (10%/100%) = (10/100) = (.10).

The formulas as I show them make use of �(� and �)� to indicate the order of operations to be performed and the grouping of terms.  Sometimes, to make the terms stand out clearer, I might use more of them than are absolutely necessary.  More than absolutely necessary still gives a correct answer, so, if in doubt as to the order of the operations, or the grouping of the terms, just use the parentheses as shown and you will get the correct solution as presented to you.
Example:
5*2 + 3 doesn�t really require parentheses because the order of calculations is the same as the default order (multiplication first, then addition / subtraction).  I might show this as (5*2) + 3 for clarity.  If you put that in your calculator as shown you will still get the correct answer (13).  If what I really meant was 5*(2+3), then the parentheses are absolutely necessary because this is different than the default order of arithmetic operations.

Sometimes formulas look different when they are not.
Example:

{{{C * (A/D) / (1/E)}}} doesn�t look like {{{(C*A*E)/D}}} but it is.

If the formula you are looking at doesn�t look like it�s the one you think it is, play with it a little to see if you can transform it using the rules of algebra into the form that is more in line with what you think.  The least you can do is use both formulas to see if you get the same answer.  That�s a fairly good test.  Same answer every time usually means you are dealing with the same formula even if it looks different.

INTEREST RATE

interest rate = percent interest / 100% (example:  10% / 100% = .1 interest rate)
For use in the financial formulas, Interest Percent always has to be converted to its decimal equivalent which I call Interest Rate.  Interest % / 100 % = Interest Rate.  Example:  (10%/100%) = (.1)

yearly interest rate = annual interest rate / 1.
quarterly interest rate = annual/yearly interest rate / 4
monthly interest rate = annual/yearly interest rate / 12
unless otherwise specified, yearly interest is assumed.
unless otherwise specified, compound interest is assumed.

SIMPLE INTEREST VERSUS COMPOUND INTEREST

If the interest rate you earn each year is NOT re-invested into the principal, then you are dealing with simple interest.
The principal is the amount you have invested.
The interest rate is what you earn on the amount you have invested.

EXAMPLE OF SIMPLE INTEREST

You invest $10,000 for 5 years at 10% simple interest rate per year.
How much do you have at the end of the 5 years?
You take the interest rate for each year and multiply it by the number of years to get the total interest and then add it to the principal.

Formula is:
{{{FV(PA) = PA + (n*i*PA)}}}
FV = Future Value
PA = Present Amount
i = Interest Rate per Time Period

Principal = $10,000
Interest for each year is not added to the principal which means that the interest for each succeeding year is calculated from the original principal resulting in the same interest calculation each year.
Yearly Cash Flow looks like this:

end of year 1 principal is $10,000 interest is $1,000.00 cumulative total is $11,000.00
end of year 2 principal is $10,000 interest is $1,000.00 cumulative total is $12,000.00
end of year 3 principal is $10,000 interest is $1,000.00 cumulative total is $13,000.00
end of year 4 principal is $10,000 interest is $1,000.00 cumulative total is $14,000.00
end of year 5 principal is $10,000 interest is $1,000.00 cumulative total is $15,000.00

What you get back at the end of the investment period is the cumulative sum of the original principal invested plus interest earned each year on the original investment.

If the interest rate you earn each year IS re-invested into the principal, then you are dealing with compound interest.

EXAMPLE OF COMPOUND INTEREST

You invest $10,000 for 5 years at 10% compound interest rate per year.
How much do you have at the end of the 5 years?
Formula is:
{{{FV(PA) = PA * (1+i)^n}}}
FV = Future Value
PA = Present Amount
i = Interest Rate per Time Period
n = Number of Time Periods

Interest for each year is added to the principal which means that the interest for each succeeding year is calculated from a larger principal resulting in a larger interest calculation each year.

Yearly Cash Flow looks like this:

end of year 1 principal is $10,000 interest is $1,000.00 cumulative total is $11,000.00
end of year 2 principal is $11,000 interest is $1,100.00 cumulative total is $12,100.00
end of year 3 principal is $12,100 interest is $1,210.00 cumulative total is $13,310.00
end of year 4 principal is $13,310 interest is $1,331.00 cumulative total is $14,641.00
end of year 5 principal is $14,641 interest is $1,464.10 cumulative total is $16,105.10

What you get back at the end of the investment period is the cumulative sum of the original principal plus the additional principal invested each year plus interest earned on the total principal each year.
Total principal is the original principal plus the additional principal added each year.
Additional principal is the interest earned on the total principal that is re-invested each year.

TIME PERIODS

yearly time periods = number of years * 1.
quarterly time periods = number of years * 4.
monthly time periods = number of years * 12.

Unless otherwise specified, yearly time periods are assumed.
The problem will usually state what the time period should represent, either directly, or indirectly.

TIME POINTS VERSUS TIME PERIODS

Time periods can be yearly, monthly, quarterly, or any other measure.   Years and months are most often used.  Sometimes quarterly time periods are used (as in bond interest calculations).

Time points represent a point in time.

Each time period will have two time points.
One time point will be at the beginning of the time period and one time point will be at the end of the time period.

Example:
Number of Time Periods is 3.
time point 0:  beginning of first time period.
time point 1:  end of first time period and beginning of second time period.
time point 2:  end of second time period and beginning of third time period.
time point 3:  end of third time period.

based on the above, time point 1 represents the end of time period 1, time point 2 represents the end of time period 2, etc.

Present Value calculations are made to the beginning of the first time period which is time point 0.
Future Value calculations are made to end of the last time period which has the same number as the number of time periods.  In the example just stated, the number of time periods is 3 and the future value calculations are made to the end of time period 3 which is the last time period.

MONEY

When entered into the formula, money should be shown as digits only without the $ sign or the comma (Example:

$100,000 should be entered as 100000)

BASIC FINANCIAL FORMULAS

Each one of these formulas will have a separate lesson for it with the title the same as shown below.
Example:  If you wish to see the detailed lesson on FUTURE VALUE OF A PRESENT AMOUNT, then look for the lesson titled FUTURE VALUE OF A PRESENT AMOUNT.

FUTURE VALUE OF A PRESENT AMOUNT
{{{FV(PA) = PA * (1+i)^n}}}
FV = Future Value
PA = present amount
i = Interest Rate per Time Period
n = Number of Time Periods

PRESENT VALUE OF A FUTURE AMOUNT
{{{PV(FA) = FA / ((1+i)^n) }}}
PV = Present Value
FA = future amount
i = Interest Rate per Time Period
n = Number of Time Periods

FUTURE VALUE OF A PAYMENT
{{{ FV(PMT) = (PMT * ((1+i)^n-1)/i) }}}
FV = Future Value
PMT = Payment per time period
i = Interest Rate per Time Period
n = Number of Time Periods

PRESENT VALUE OF A PAYMENT
{{{ PV(PMT) = (PMT * (1 - (1 / (1+i)^n))/i) }}}
PV = Present Value
PMT = Payment per time period
i = Interest Rate per Time Period
n = Number of Time Periods

PAYMENT FOR A FUTURE VALUE
{{{ PMT(FV) = (FV / (((((1+i)^n-1))/i))) }}}
PMT = Payment per time period
FV = Future Value
i = Interest Rate per Time Period
n = Number of Time Periods

PAYMENT FOR A PRESENT VALUE
{{{ PMT(PV) = (PV / ((((1 - (1 / ((1+i)^n))))/i))) }}}
PMT = Payment per time period
PV = Present Value
i = Interest Rate per Time Period
n = Number of Time Periods