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Interest-bearing Bank Accounts & Inflation Part I-Math w/Business Apps, Compound Interest Chapter - YouTube
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Interest-bearing bank accounts dealing
with compound interest. The first
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objective will be looking at the
different types of interest bearing
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accounts. We have regular savings
accounts this is generally the type of
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savings accounts were introduced to as a
child.
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They are easy to use, the positive is that they're
liquid which means you deposit money
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today you can take that money out
tomorrow. There's no time restriction on
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it. Because they're found at a bank
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most banks are FDIC which stands for
Federal Deposit Insurance Corporation. In
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the event that the bank should go out of
business
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the FDIC insurance kicks in and will
give you your money up to $250,000. The
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downside is they are very low interest
rates. And here's a table from a bank
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showing what a regular savings account is
requiring there be $100 in the
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savings account. And they're earning
one tenth of one percent interest rate
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on it. So not very high at all but again
some of those other pluses outweigh the
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interest being paid. We also have
checking accounts that will pay interest
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which is definitely a plus provided you
have a balance in your account. And this
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may or may not be a positive but to earn
the interest you need to carry a
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minimum balance. When that minimum balance
isn't maintained and there could be a fee
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assessed. So be sure when you are looking
at opening up a new checking account
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that you check into the options and what
seems to fit your financial situation.
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So let's look at how we compute daily
interest. Sometimes we will have interest
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savings accounts that pay
compound interest daily. We'll see them
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in savings accounts, passbook savings, or
checking accounts that pay interest as
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well. We can use the formula that we use
for compound interest that we saw
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previously. And here is an example if we
have $500 at 4% compounded
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daily for 3 years this is what the
formula would look like.
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Here's our principal times the quanity one plus our
interest rate as a decimal divided by
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the compounding period which is daily.
So we use 365 days raised to the "n" the number of
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compounding periods 3 years at 365
per year which results in the amount of
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$563.74. Or we can use a table, on the
table we would look at something that is
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set up for compounded daily and then the
interest rate that the account is paying.
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Similar to compound interest tables that
we've seen in previous sections we'll
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pull that value from the table which
replaces the quantity that's shaded here
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in our compound interest formula. But
leaves us with multiplying that value by
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the principal amount to give us our
answer. Here's an example of a compound
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interest table for daily frequency and
it's set at a 3.5% interest
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rate. Very similar to the table that
we've seen before the columns in blue
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are the number of days and adjacent to
it is the value that we will use to
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replace this portion of our compound
interest formula.
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So here we have an example set aside
$5,500 in his savings account earning
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3.5% interest compounded daily
for 50 days. How much interest will
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be earned?
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We could use our formula or using this
table we need to make sure that we're
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using the appropriate table. This is set
for 3.5% interest and compounded
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daily which is the case for this problem.
So our next step will be to find the
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number that corresponds with 50 days.
Here on the third column of 'Number of Days'
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we find 50 the number adjacent to it
will replace this portion of our
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compound interest formula. Which leaves
us only to take the principal times
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that value to give us the total amount
in the account after 50 days. Let's look
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at another one, $3200 dollars is invested in a
savings account earning 3.5%
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interest compounded daily for 85
days. How much interest will be earned?
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We're still dealing with compounded
daily at 3.5%, so we use this table we're going to
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locate where 85 is with our multiplier.
Multiplying our deposit by that value from
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the table gives us our total amount in
the account after 85 days. But the
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problem is asking how much interest is
earned. We will take our balance at 85
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days and subtract the initial
deposit to determine the amount of
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interest that's earned in the account.
Let's take a look at maybe a more
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practical problem in the sense that
deposits are added periodically and
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we're interested in what amount would be
after a certain amount of time or maybe
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we have withdraws taken. So in this first sample
problem we're going to use the 3.5%
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interest compounded daily. On January 1, this bank was opened and
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the amount of $8,756 was deposited, in
February another amount and in March a third
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amount was deposited. And the question
is asking, what is the balance on March
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31 and ultimately what
is the interest earned? So we're going to take this
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as though it were three separate
problems. Here we have our timeline we need to
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know how many days this first deposit is
going to be in there. If nothing else
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happened in this account on January 1
this amount was deposited and we're
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interested in how much money that
accrued due to compound interest being
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paid daily on March 31. Well if we do
the calendar math there are 90 days
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between March 31 and January 1. So
we'll use our table with the 3.5%
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interest for compounded
daily, we'll find our multiplier
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that is associated with the
90 days and multiply that initial
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deposit. So this would be the balance
after the 90 days for just that first
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deposit. Then we'll go to the
February 11th deposit this money is
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sitting in here from February 11 until
March 31 it too will be accumulating
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interest but only from February 11
until March 31, which is 48 days. To
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calculate the interest earned on that
amount we will look up 48 days on our
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table, which this is our multiplier times
it by that
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deposit that's only sitting in the account
for 48 days and we have the
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ending balance. The last step here is
looking at how long is the March 21st
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deposit of $650 in the account and
earning interest. Well March 21 to
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March 31 is 10 days. The
interest earned on that account and the
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ending balance for that deposit is this
multiplier times 650. Now if we add these
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3 values together it will give us
the balance from these 3 separate
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deposits on these different dates. That
answers the first question. To determine
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the amount of interest we need to take
this balance and subtract off those
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principal deposits that were made
through the course of this 90
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period. So here's what that would look
like we take our balance after the
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90 days
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subtract each of those three. And here
we're showing that they added those 3
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principal deposits and then subtracted
that quantity from the balance as of
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March 31. The result is an earning of
$80.82. Here's another example where we
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have some withdraws that are occurring,
so let's take a look at this one. On
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April 1 MVP Sports opened a savings
account with a deposit of $17,500. A
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withdrawal of $5000 was made 21 days later, and another
withdrawal of $980 was made 12 days
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before July 1. Find the balance on July 1.
To solve a problem with a
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withdrawal we kind of reverse our thinking a
little bit to calculate this. On 21 days
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past this initial deposit $5000 was
withdrawn. Which means that $5,000 sat
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there for the first 21 days before it
was moved or withdrawn and it was
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earning interest. We have another
withdrawn made 12 days before July 1st.
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Doing some calculation that means that
this $980 sat in there from April 1
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until 12 days before July 1.
Which would apparently if we do that
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calculation July 1 is 182nd day of the
year, 12 days before that is 170th day.
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April 1 is the
91st in the difference between the 170th
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and 91st is 79 days.
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So this $980 before it was withdrawn was
compounding interest every day for 79
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days. What stayed in the account the
entire period from April 1 to July 1 is
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the difference between the initial
deposit and these two withdrawals. So if
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you take that initial deposit and
subtract the two
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withdraws that were made this means
there was this amount of money that was
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left in the account for that time period
from April 1 to July 1. We then need
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to calculate what the balance is for
each one of these three values: $5,000
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times we'll look up the number from our
table associated with 3.5%
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interest compounded daily for 21
days this is what this would have grown
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to. For $980 sitting in their 79
days we find the
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multiplier and the multiplier associated
with 91 days, which is actually below the
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table in a little note there's where
you'll find your multiplier for that.
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These then are what the balances are for
these accounts with their interest. We're
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almost done, what we need to do is add the 3 up
but recognize we did withdraw the
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$5,000 and the $980 which gives us an
ending amount of $11,638.49. You could
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have subtracted your $5000 off
from here to get a $10.08 interest
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earning on that amount sitting for 21
days before the withdrawal. And if we
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take our $980 withdrawal away from here
it means it earned $7.45. We could have
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added the interest from these two onto here and
still arrived at that same value.
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