In this video we're going to be discussing the basic time value concepts.
Particularly we're going to be looking at simple interest versus compound
interest. So let's first look at simple interest. Now a simple interest as we
discussed early in an earlier video it's interest computed only on the principal.
So you're not really earning interest on interest. Using this illustration
Barstow Electric Incorporated borrows $10,000 for three years at a simple
interest rate of eight percent per year. We need to compute the total interest to
be paid for year one. So remember your computation for interest is principal
times rate times time. So in this case we would take our principal of $10,000
dollars times our percentage rate times the period which in this case is is
three years. But for year one we just want the interest for one period which
is eight percent. Keep in mind that interest rates are given on an annual
basis so that's very important when we're looking at partial years' interest.
Alright so for year one it would be $800. So for three full
years the interest would be 10,000 times 8% (0.08) times the periods which is
three periods is $2400. So again it's it's simple interest in this case
because it is an annual basis. But what if we have a partial period. So for
example if Barstow borrows $10,000 for three months at eight percent per year
the interest rate is computed like this: we would take the interest rate times
the principal times the time, so remember interest rate is given on an annual
basis so we have to convert our periods to annual. We're only three periods, so to
convert that to annual or to years it would be 3 out of 12 months okay or
one-fourth of a year. So in this case the interest would be $200
for the three months. Now compound interests we remember is not only
earning interest on the principal but we also earn interest on the interest that
we have accumulated up to that point. Let's look at an example with Eagle
Company they deposit $10,000 in the Last National Bank where it will earn simple
interest of 9% per year. It deposits another $10,000 in
the First State Bank where it will earn compound interest of 9% per
year compounded annually. In both cases Eagle will not withdraw any interest
until three years from the date of deposit. So this example is giving us all
the same information, two different banks, one's paying simple interest, one's paying
compound interest. So let's just see what the difference will be over three years.
On the left at the Last National Bank you can see that each year we are
earning $900 in interest because we're earning 9% on
the principal only. So every year even though at the end of year one we've
accumulated $10,900 in that account. At the start of
year two we're earning interest on the principal of $10,000. So at the
end of the year two we'll have $11,800 which is our $10,000 principal plus
$1800 in total simple interest at that point. Now if you look
over at the First State Bank that's paying compound interest year one is the
same as simple interest. We're earning 9% on $10,000. But
if you look at year two, we're earning 9% on $10,900
$10,900 which is including the principal and the interest that we
earned in year one. So now at the end of year two we have $11,881 dollars
so $81 dollars more at the end of year two for compound interest than we had under
simple interest and by the end of year three we have over $250
dollars more under compound interest at the First Bank than we have under simple
interest at the Last Bank. When we're dealing with time value of money
concepts we have a really great tool that we can use and it's the time value
of money tables that we have. So let's look at this one for example. Now this is
the future value of a lump sum table and you can see in year one just like we saw
in the prior screen at 9% we multiply the principal times 1.09 that's
109% of the principal. But look at year two. Year two
we would multiply the principal times 1.1881 for 9%.
Now what that number has incorporated like for example if I want
to know how much I would have in the bank at the end of two years if I
deposited however much money, I would multiply that amount of money that I'm
going to deposit by 1.1881 and that would tell me how
much I would have at the end of year two under compounding interest because that
number that factor it includes not the principal but it includes the
periods and the interest rate over two years in that number what would
accumulate over time. Okay so it's a very handy tool and it makes things really
quick when we're looking at time value of money concepts. Another topic we have
to have to be cognizant of is this idea of compounding. Things are not always
compounded annually. They may be compounded semi-annually or quarterly or
monthly. In this case you have to figure out your periods because when you look
at the time value of money tables if it's compounded semi-annually you
basically have to double your periods. So looking at this chart here if you look
at semi-annually, if your interest rate is 12% then compounded
semi-annually your interest rate is actually 6% over 10 periods in
this case because we're looking at five years compounded semi-annually. So you
actually have 10 periods because you've got two periods per year so you've got
to divide your interest rate in half in this case to get 6%. If you're
looking at a 12% annual interest rate compounded over five years
monthly then your interest rate would be one
percent over 60 periods so 12 periods per year. Also under time value of money
it's very handy that we don't only just look for the present value and future
value amounts. We maybe we may know the present value and the future value and
need to find out well how long do I need to keep it there? So the number of
periods you may have to solve for the number of periods. In addition you can
use the time value of money information and the time value of money tables to find
the necessary interest rate to make those numbers happen.
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