Hi, welcome back to Finance for Non- Finance Professionals.

In this short video in week one,

I'd like to talk a little bit about the difference between

effective and nominal interest rates.

We've talked about interest rates generally,

but they go by lots of terms and there's lots of

different nomenclature in terms that people use in practice,

and a lot of students sometimes get confused when

we talk about whether we cut interest rates in half or

compound them and so that comes down to

the definition of whether we're talking about an effective,

or a nominal interest rate.

The nominal rate, is the rate that you usually see the bank state on a mortgage.

If a bank says that they're charging 5 percent on their 10-year mortgages,

that means that's a stated rate or what's

sometimes called an annual percentage rate or APR.

That's the periodic rate times the number of periods.

So, if you were paying one percent a month,

you'd be paying 12 percent a year.

If you were paying two percent a quarter,

you'd be paying two times four quarters or eight percent per year.

The effective rate is how much you would actually earn,

if you earned that periodic rate including the interests in a compounding.

So, rather than taking that annual rate and dividing it by the number of periods,

the effective rate is a compound annualized rate.

So lots of times when we do problems,

or we work through what we see in practice differ sometimes stated rates,

it can be different from the rate that you earn which is the effective rate.

The effective rate is the rate that really as an investor matters,

or as a borrower,

if I'm taking out a mortgage,

the effective rate is the rate that you're actually

paying once you include all the compounding.

So, let's think about what this would look like in practice.

We'll just walk through an example.

If there was monthly compounding let's say,

and there was a nominal or stated rate of six percent that,

let's say it was compounded monthly,

which means that the rate every month, the stated rate,

would be just that six percent divided by the number of periods,

12 months, so 12 periods,

which would give you about 0.5 Percent.

One half of one percent every month.

With compounding though, you won't exactly be

six percent because each month you're earning

interest on the interest that you earned the previous month,

and so once you include that and compound it,

using the formula that we learned in the last lecture,

it would be one plus that one half percent raised to the 12th power.

So 1.0617, or an effective rate of 6.17 percent.

That little extra scooch,

that little 0.17 makes the effective rate

larger than the annual percentage rate or stated rate or nominal rate.

Now that can be very important as we go along into long periods.

Generally, if we take that formula that we just did in the previous example,

and make it formulaic or generic,

for any period, for any rate.

What we're going to do is, we're going to take the nominal rate,

divide it by the number of periods, add one to it,

that's one plus r, and then raise that to

the power of n the number that we divided by to get to an effective rate.

Generally, the effective rate is larger than the nominal rate.

Now, you know that's true because most of the times a bank will tell

you what it's paying its depositors as

an effective rate to try to juice up what you're actually going to earn,

but state all their mortgages and nominal rates because

it's actually a little bit lower and makes it seem like you're paying less.

In practice, what you're actually

earning when you put money in the bank is the effective rate.

When you take out a mortgage or a loan,

what you are actually paying in compounded interests,

the number of dollars moving out of your account,

is the effective rate.

Again, the nominal rate or stated rate,

is just that periodic rate divided by the number of periods.

The effective rate, is the compounded rate that includes the periodicity of compounding.

I just wanted to get that nomenclature right for everybody so

that you can understand sometimes in practice's or problems are in

the field when you see sometimes domino rates and they're

divided by the number of periods and then effective rates are compounded,

it's not that one is right and one is wrong,

it's just that there's really two definitions in practice.