Kinds of Interest Rates

Let's say I give you a credit card and the interest rate on the card is 3% per month. What is the annual rate that you are actually charged?? 36%?? Well, no. It's actually 42.57%.

Nominal Rate Nominal means "in name only". This is sometimes called the quoted rate.
Periodic Rate The amount of interest you are charged each period, like every month.
Effective Annual Rate The rate that you actually get charged on an annual basis. Remember you are paying interest on interest.

In the example
The Nominal Rate is 36%.
The Periodic Rate is 3% (you are charged 3% interest on your balance every month)
The Effective Annual Rate is 42.57%
Nominal Rate = Periodic Rate X Number of Compounding Periods
Effective Annual Rate = (1+ i / m)m -1

m = the number of compounding periods
i = the nominal interest rate
O.K., so let's try the example again.

Effective Annual Rate = (1+ i / m)m -1
Effective Annual Rate = ( 1 + .36 / 12 )12 -1
Effective Annual Rate = (1.03)12 - 1
Effective Annual Rate = (1.4257) -1
Effective Annual Rate = .4257
Effective Annual Rate = 42.57 %

Perpetuities

Perpetuities - are equal payments made regularly, like every month or every year, that go on forever.

You are rich. (Yes, but are you really happy?) You want to start the YOUR NAME HERE Scholarship at your university. Every year, some student will receive a $1000 scholarship. You're paying for it. Even after you, your kids and your grandkids are dead, you are still paying for it. Forever.

The question is....How much money will it cost you. In today's dollars. What is the present value of this perpetuity. (Hint: starting now and going on forever and ever, you assume the interest rate at your bank is going to be 3%).
PV (of a perpetuity) = payment / interest rate


Every year the interest you earn is used to pay for the scholarship. The principal in your bank account doesn't really change year to year.

PV (of a perpetuity) = payment / interest rate
PV = $ 1000 / .03
PV = $ 33,333
So, you put $ 33,333 into the bank. Each year the money earns $1000 interest. That interest becomes the scholarship.

The Time Value of Money

Present Value How much you got now.
Future Value How much what you got now grows to when compounded at a given rate

I give you 100 dollars. You take it to the bank. They will give you 10% interest per year for 2 year.

The Present Value = $ 100
Future Value = $121.
FV= PV (1 + i )N

FV = Future Value
PV = Present Value
i = the interest rate per period
n= the number of compounding periods