Interest-bearing bank accounts dealing

with compound interest. The first objective will be looking at the

different types of interest bearing accounts. We have regular savings

accounts this is generally the type of savings accounts were introduced to as a

child. They are easy to use, the positive is that they’re

liquid which means you deposit money today you can take that money out

tomorrow. There’s no time restriction on it. Because they’re found at a bank most banks are FDIC which stands for

Federal Deposit Insurance Corporation. In the event that the bank should go out of

business the FDIC insurance kicks in and will

give you your money up to $250,000. The downside is they are very low interest

rates. And here’s a table from a bank showing what a regular savings account is

requiring there be $100 in the savings account. And they’re earning

one tenth of one percent interest rate on it. So not very high at all but again

some of those other pluses outweigh the interest being paid. We also have

checking accounts that will pay interest which is definitely a plus provided you

have a balance in your account. And this may or may not be a positive but to earn

the interest you need to carry a minimum balance. When that minimum balance

isn’t maintained and there could be a fee assessed. So be sure when you are looking

at opening up a new checking account that you check into the options and what

seems to fit your financial situation. So let’s look at how we compute daily

interest. Sometimes we will have interest savings accounts that pay

compound interest daily. We’ll see them in savings accounts, passbook savings, or

checking accounts that pay interest as well. We can use the formula that we use

for compound interest that we saw previously. And here is an example if we

have $500 at 4% compounded daily for 3 years this is what the

formula would look like. Here’s our principal times the quanity one plus our

interest rate as a decimal divided by the compounding period which is daily.

So we use 365 days raised to the “n” the number of compounding periods 3 years at 365

per year which results in the amount of $563.74. Or we can use a table, on the

table we would look at something that is set up for compounded daily and then the

interest rate that the account is paying. Similar to compound interest tables that

we’ve seen in previous sections we’ll pull that value from the table which

replaces the quantity that’s shaded here in our compound interest formula. But

leaves us with multiplying that value by the principal amount to give us our

answer. Here’s an example of a compound interest table for daily frequency and

it’s set at a 3.5% interest rate. Very similar to the table that

we’ve seen before the columns in blue are the number of days and adjacent to

it is the value that we will use to replace this portion of our compound

interest formula. So here we have an example set aside

$5,500 in his savings account earning 3.5% interest compounded daily

for 50 days. How much interest will be earned? We could use our formula or using this

table we need to make sure that we’re using the appropriate table. This is set

for 3.5% interest and compounded daily which is the case for this problem.

So our next step will be to find the number that corresponds with 50 days.

Here on the third column of ‘Number of Days’ we find 50 the number adjacent to it

will replace this portion of our compound interest formula. Which leaves

us only to take the principal times that value to give us the total amount

in the account after 50 days. Let’s look at another one, $3200 dollars is invested in a

savings account earning 3.5% interest compounded daily for 85

days. How much interest will be earned? We’re still dealing with compounded

daily at 3.5%, so we use this table we’re going to locate where 85 is with our multiplier.

Multiplying our deposit by that value from the table gives us our total amount in

the account after 85 days. But the problem is asking how much interest is

earned. We will take our balance at 85 days and subtract the initial

deposit to determine the amount of interest that’s earned in the account.

Let’s take a look at maybe a more practical problem in the sense that

deposits are added periodically and we’re interested in what amount would be

after a certain amount of time or maybe we have withdraws taken. So in this first sample

problem we’re going to use the 3.5% interest compounded daily. On January 1, this bank was opened and the amount of $8,756 was deposited, in

February another amount and in March a third amount was deposited. And the question

is asking, what is the balance on March 31 and ultimately what

is the interest earned? So we’re going to take this as though it were three separate

problems. Here we have our timeline we need to know how many days this first deposit is

going to be in there. If nothing else happened in this account on January 1

this amount was deposited and we’re interested in how much money that

accrued due to compound interest being paid daily on March 31. Well if we do

the calendar math there are 90 days between March 31 and January 1. So

we’ll use our table with the 3.5% interest for compounded

daily, we’ll find our multiplier that is associated with the

90 days and multiply that initial deposit. So this would be the balance

after the 90 days for just that first deposit. Then we’ll go to the

February 11th deposit this money is sitting in here from February 11 until

March 31 it too will be accumulating interest but only from February 11

until March 31, which is 48 days. To calculate the interest earned on that

amount we will look up 48 days on our table, which this is our multiplier times

it by that deposit that’s only sitting in the account

for 48 days and we have the ending balance. The last step here is

looking at how long is the March 21st deposit of $650 in the account and

earning interest. Well March 21 to March 31 is 10 days. The

interest earned on that account and the ending balance for that deposit is this

multiplier times 650. Now if we add these 3 values together it will give us

the balance from these 3 separate deposits on these different dates. That

answers the first question. To determine the amount of interest we need to take

this balance and subtract off those principal deposits that were made

through the course of this 90 period. So here’s what that would look

like we take our balance after the 90 days subtract each of those three. And here

we’re showing that they added those 3 principal deposits and then subtracted

that quantity from the balance as of March 31. The result is an earning of

$80.82. Here’s another example where we have some withdraws that are occurring,

so let’s take a look at this one. On April 1 MVP Sports opened a savings

account with a deposit of $17,500. A withdrawal of $5000 was made 21 days later, and another

withdrawal of $980 was made 12 days before July 1. Find the balance on July 1.

To solve a problem with a withdrawal we kind of reverse our thinking a

little bit to calculate this. On 21 days past this initial deposit $5000 was

withdrawn. Which means that $5,000 sat there for the first 21 days before it

was moved or withdrawn and it was earning interest. We have another

withdrawn made 12 days before July 1st. Doing some calculation that means that

this $980 sat in there from April 1 until 12 days before July 1.

Which would apparently if we do that calculation July 1 is 182nd day of the

year, 12 days before that is 170th day. April 1 is the

91st in the difference between the 170th and 91st is 79 days. So this $980 before it was withdrawn was

compounding interest every day for 79 days. What stayed in the account the

entire period from April 1 to July 1 is the difference between the initial

deposit and these two withdrawals. So if you take that initial deposit and

subtract the two withdraws that were made this means

there was this amount of money that was left in the account for that time period

from April 1 to July 1. We then need to calculate what the balance is for

each one of these three values: $5,000 times we’ll look up the number from our

table associated with 3.5% interest compounded daily for 21

days this is what this would have grown to. For $980 sitting in their 79

days we find the multiplier and the multiplier associated

with 91 days, which is actually below the table in a little note there’s where

you’ll find your multiplier for that. These then are what the balances are for

these accounts with their interest. We’re almost done, what we need to do is add the 3 up

but recognize we did withdraw the $5,000 and the $980 which gives us an

ending amount of $11,638.49. You could have subtracted your $5000 off

from here to get a $10.08 interest earning on that amount sitting for 21

days before the withdrawal. And if we take our $980 withdrawal away from here

it means it earned $7.45. We could have added the interest from these two onto here and

still arrived at that same value.