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Interest-bearing Bank Accounts & Inflation Part II-Math w/Business Apps, Compound Interest Chapter


In this section will look at time deposit accounts and inflation. Another type of
account that pays interest is called a certificate of deposit. The good
positives for a CD is generally they’re issued from a bank that has the Federal
Deposit Insurance Corporation backing in the event that the institution goes out of
business you will get your money out of that. They do pay a higher interest
rate than a regular savings account or an interest bearing checking. Part of a
certificate of deposits’ requirement is that the money needs to
be in the account for a designated amount of time. And it can be as short as
perhaps 3 months and as long as 5 years or even longer. The downside is it does require a minimum
deposit. The bank is counting on this money being there, a substantial amount of
money being there so that they can in turn then use it to make money on your
money. And should you need this money and withdraw before the maturity date it is
subject to a penalty which is typically the last interest or so that’s earned.
Here’s a table of some CD rates being paid currently we can see here we have
3 months at $500 is earning 1/10 of 1%. If we drop down we
can get a .35% for a 2 year CD but a $10,000 minimum
deposit needs to be made. And here at the bottom to get a 1.25% interest
rate you need to sign up for a 5 year deposit of $10,000 or more. Compound interest table for longer
periods we will look at daily compounding for more than just 1 day
up to 90 days. And we need a table for that we can always use the formula but
the table saves a little bit a of time and here we have a table showing the
number of years and the interest rates for the compounded daily. In this example
W.C. wants to deposit $4,000 his account is paying 5% compounded daily
certainly not something that’s happening for us currently. And the question is
should he leave it in there for 2 or 3 years? So we will determine what
that value is for both of those possibilities. Using the compound
interest for time deposit accounts compounded daily we’ll look up two years
and corresponding with 5% here’s our multiplier. We’ll times that by $4000
and see that the account has grown to $4420.65. If the
money is in there for another year tied up can you stand to not have access to
that money versus the gain in this account. And we’re talking a little over
$200 additional interest is earned by having it in there in three years. And
this is a decision you need to make when you’re taking out a certificate of
deposit. Know that you don’t want to put money into an account for 2 or 3 or 5 years whatever the case may be that it’s your emergency money that you
may need to pull it out. It’s much better that you know you won’t
be replacing the car you have emergency funds available to you and so that you
won’t be cashing out. Not that it’s the worst thing in the world but you should go with shorter lengths of time
and sacrifice your interest rate to avoid having to cash out early and
paying a penalty. The other topic in this section is dealing with the consumer
price index which is a measure of our inflation. An inflation is a rise in
general price levels of goods and services. And we can illustrate here what
inflation actually does. In 1950, if you had $100,000 today or at least in 2015
you would need almost a million dollars to have the same purchasing power that
you did in 1950, sixty-five years later. The measure of inflation
here in the United States is called the consumer price index and it’s based
on a series of standard goods and services. It’s a common bundle that they
calculate from one year to the next. What is your electricity bill and certain
groceries and commuting and so on. And just for your information here, last year 2015
for the 12 months running the United States inflation rate was 0.7%.
So let’s take a look at what happens when we have a current
income and there’s no raise but we have an inflation or consumer price index
increase of 4%. If that was the case, this individual would have to have instead of
$23,000 they would have to have $23,920 to have the same buying power
because of that 4% inflation factor. And where is the $920 coming from?
If you take the current salary times the inflation factor of 4% as a
decimal times one year that means we have an increase of $920. So what if you
didn’t get that corresponding 4% raise? It means you will need to trim $920 out
of your current budget so that you can stay status quo and not be short on
being able to pay your expenses and live at the standard that you previously were.
If we have a current income of $23,000 and we saw a 4% consumer price index we
know we need $920. But what if, you received a 2.4% raise? Well it’s not what you need to
keep up with inflation but at least you’re not as far behind. And that $23,552 comes from taking the beginning salary $23,000 times the
wage increase of 2.4%, expressed as a decimal for a year is $552. So if someone received a
2.4% raise its better than no raise but it’s still not keeping up with the
inflation rate for that year. And so if we look at what the 4% does compared to the
2.4% raise there’s still $368 drop in buying power. To keep your level of
lifestyle the same you would need to cut $368 worth of
expenditures to maintain your status quo. Here we have another example, someone has
$1,800 in a savings account for 1 year that pays 3.5% interest
compounded daily. What is the loss or gain in purchasing power if the consumer
price index went up 3.9%? We can see right now the interest is not high
enough keeping up with the inflation factor here so there will be a loss but
let’s calculate it out. We have another table for 3.5%
interest compounded daily only expressed in quarters and one year would be four
quarters. So here we have a multiplier we will find the maturity value of that
$1,800 times 4 quarters which would be the one year for the 3.5%
interest compounded daily. So after one year the balance in this
account would have this value (1863.22) and if we subtract off that principle of $1,800 it
has made $63.22 in interest in the past year. What is the result or the
impact of the inflation factor 3.9% on our $1800? We’ll take 1800 times
.039 the decimal equivalency of 3.9% and we see that the gain to have still the
same buying power of the $1800 needed to have an increase of $70.20. We can take
the difference right here between the interest gained and what the inflation
factor or the buying power now of $1800 is a year later. Or we can compare the
inflation value of our $1,800 compared to putting it in a savings account.
Either way the difference between those 2 is a loss of almost $7 in buying
power.

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