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Compute Principal, Rate, and Time – Math with Business Applications, Simple Interest Chapter - YouTube
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Math with business applications simple
interest section 2. In this section
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we're going to use our simple interest
formula, but instead of just calculating
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interest we will be given interest along
with two other of the variables and solve
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for the fourth variable. So it's a review
in the first section we took our
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principal are rate, and our time multiplied
the three values together to give us
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interest. In this section as I said we
will be solving for the principal, and
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here we have a formula circle that will
give us the other three versions for
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finding the missing variable. If we're
looking for principal cover-up principal
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and what is left is interest over rate
times time. If we're solving for rate
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cover-up rate, and what's left is
interest over, or divided by principle times time. The
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third possibility is to solve for time
when we cover up or blank out time that
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leaves an I over P times R and this
gives us the relationship, or the
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equation that will use to solve for a
time when we're calculating simple
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interest. We can also use this formula
circle to calculate interest from the
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first section if you would cover up
interest that leaves the principal rate
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time
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adjacent to one another, and as we saw in
the first section we multiply those
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three values together so let's look at
some examples. Before we do that we need
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to talk about bankers interest, are time
has to be
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expressed in terms of a year, and if that
term or the length of the loan is given
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in days we need to convert it into a
portion of a year,
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and we will use 360 days for the number
of days in any year. So these first set of
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problems that we will look at involves
finding the principal we're given the
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rate, time, and interest.
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The question is what is the principal
using our formula circle if we cover-up
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principle that leaves an I interest over
R times T plugging in the values given
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in this problem in place of I we put the
interest 355 interest rate expressed as
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a decimal is here in the denominator
.085 times time expressed as a year
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and since they gave it to us as days we
can, or must convert this into a portion
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of a year, and that's why we have the
denominator 360. This looks a little
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intimidating in the fact that we have a
fraction in the denominator anytime in
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the math world if you have a fraction in
the numerator, or the denominator we call
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this our both we call this a complex
fraction there are several ways that you
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can handle this will see any second how
you can simplify the denominator, and
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once we have that value will take the
numerator divided by this simplification
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of the denominator, or we can do this
all-in-one calculation if we put
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parentheses around the denominator so one
option would be to enter 355 in your
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calculator divided by, and then we need
to tell the calculator that we're
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dividing by an expression so we would
hit the left
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parentheses .085 times 65
divided by 360 with the end parentheses
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and hit or equals to give us our final
answer, or as I said step-by-step follow
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order of operations
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you have an option of do the calculation
here
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.085 times 65 divided by 360 results in
this value, and our final calculation is
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you'll either need to store this value or
write it down because we need to start
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with the numerator 355 divided by the
denominator resulting in $23,131.22
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now we need to be aware that this is
money and if necessary rounded to the
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nearest cent one other caution about
rounding if you go the route of
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simplifying the denominator, and writing
down this number be cautious of rounding it
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too short because when you enter your
values in stat-crunching may find you
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are not getting the correct answer even
though you're calculating it correctly
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rounding to abruptly or too early and a
problem will result in an incorrect
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answer. Here's another one asking us for
principle this time the time is in
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months so we'll have to be sure we
convert that into an equivalent
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expression of time in terms of years how
do we solve for principal blocking out
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the P in this circle formula that
leaves us with I interest over rate times
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time replacing those variables with the
information given interests of 295 is
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the charge on this loan the interest
rate R as a decimal and as a just set
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a minute or so ago our time in terms of
year we will take our five months over
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twelve. You have the choice of how you
want to simplify this simplify the
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denominator or enter it as one long
string in your calculator, and to do that
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we would put parentheses around the
values in the denominator so again just
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repeating how to do that it would be 295
divided by left or beginning parentheses
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.0615 times
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5 divided by 12 and paren and hit the equals you
wouldn't see this detailed information
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but you should see this final answer. If
you choose to simplify the denominator
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here's the value we get and again we
need to take 295 divided by that
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simplification of original formula to
get the correct answer. Next we'll take a
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look at solving for the rate very
similar arrangement of our variables
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when we cover up rates says that to
calculate it we will take our interest
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divided by principal times time replace
those variables with the values given
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the interest in this problem is $16.53
P needs to go on the denominators so we
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will put 2800 in place of the principal
and it is being multiplied by time the
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problem is giving is 85 days and so we
use the bankers rule of 360 days in a year.
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This is no different than the previous
problem solving for principle as far as
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how you're going to simplify it you can
choose to simplify the denominator and
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then take the numerator divided by that
simplified value, or use the parentheses
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and do this and all one continuous
calculation, either way we should end up
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with a value that looks like this.
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The rate calculation looks a lot like
the principal with one exception we're
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not done your rate needs to be expressed
as a percent so we need to move our decimal
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place two places to the right, and then we
may be asked to round our answer to the nearest
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tenth of a percent we don't do the
rounding for a final answer until we
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have converted this decimal to a percent
then we'll worry about the rounding, and
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having the answer in the correct form.
So when we simplify .025
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we end up with a 2.5 percent rate for
this
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example. Here we have another example
given this information they're asking us
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to find rate the relationship to
calculate rate is just like the last
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problem
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interest divided by Principal times time.
The only thing in this problem is that
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instead of giving us a specified number
of days we need to do a little bit of
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calendar math to calculate that so we'll
take the later date in the year which is
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June 10th. It corresponds with 160 first
day subtract the earlier date in the
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year from the start of this loan March
15th corresponds with seventy fourth day
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of the year when we subtract those the
term or length of loan is 87 days
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this will need to be
expressed in terms of a year so in the
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numerator we need to have our interest
in the denominator P for principal times
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T for time expressed in terms of a year, no different than the previous ones your
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choice how you decide to simplify this
it's certainly up to you but we have the
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same issue here we end up with a decimal, and we want this answer or our rate
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expressed as a percent so we will move
the decimal two places to the right, and
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only then would we round this to the
nearest 10th so we're looking at 3.79
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percent, and if they want it to the
nearest tenth of a percent the four is
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not enough to alter are seven, and we would call this 3.7%. The last calculation that
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we will look at is finding the time, in
this example were given that Roberta
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deposits $5,750 in an account paying
2.8% and she earned $65 in interest find
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the number of days that the deposit earned the interests so were given principal rate,
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and interest and we've turned this
around savings accounts where we're
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depositing the money, and earn interest
on that deposit are just calculated the
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same way as though we were borrowing
money and paying the interest charged
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for the use of that money.
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The problem is asking us for time, the
arrangement using our circle formula gives us that to
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calculate time we will take interest
divided by principal times rate. Replace
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principal and interest and rate no real
special handling other than if you're
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going to do this in one calculation you
will need to put your parentheses and
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remember times in terms of a year now
most of us probably don't know what that
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equates to in how many days it's a
little less than half a year which would
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be 180 days we can ballpark it. But the
problem is not asking us the time in
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years they're asking us for the time in days we need to convert this answer which is
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in years into days and to do that
to cancel out our years we will have to
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multiply by 360
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which gives us a time of 145 days. In
this last problem the Centerfield
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Chamber of Commerce deposited $12,000 at 3.5% and earned $245 and interest this
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is another example of a savings versus a
borrowing application the problem here
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is asking us time in terms of the
number of months so take a look at how
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we calculate this were solving for T are formula then is the interest $245 over the
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principal times the rate your choice as
far as simplifying this expression. This
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answer is in years and just like the
last one we need to convert this into
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months but instead of multiplying by 364
days we will multiply by 12 months
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because, there are twelve months in one
year the years will cancel out taking this value,
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and I should caution you again when
you're using stat-crunch don't around
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this result I would just leave it in the
calculator then multiplied by 12, and
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round as necessary with your final
answer its always a good idea to only
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round on your final step.
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