Changes

If you asked me to loan you $1000, then I might answer: why?  What’s in it for me?  You would then say that you promise to give it back.  I would then say why should I give it to you in the first place?  If I just keep the money, then I won’t have to worry about your giving it back.

If you asked me to loan you $1000, then I might answer: why?  What’s in it for me?  You would then say that you promise to give it back.  I would then say why should I give it to you in the first place?  If I just keep the money, then I won’t have to worry about your giving it back.

You would then offer to pay me money in exchange for loaning you $1000.  We would bargain.  You might offer me $25.  I might reply that is not enough for me to go the trouble and take the risk to loan you $1000.  Then you might offer me $50.  I might wonder if I can get a better deal somewhere else.  Ultimately we might settle on an amount that makes it worthwhile for me and advantageous for you.  Some states have limits on how much interest can be charged.  ''Query'': should laws limit the amount of interest that can be charged?

You would then offer to pay me extra money in exchange for loaning you $1000.  We would bargain.  You might offer me $25.  I might reply that is not enough for me to go the trouble and take the risk to loan you $1000.  Then you might offer me $50.  I might wonder if I can get a better deal somewhere else.  Ultimately we might settle on an amount that makes it worthwhile for me and advantageous for you.  Some states have limits on how much interest can be charged.  ''Query'': should laws limit the amount of interest that can be charged?

If I agreed to loan you $1000 for an extra payment by you of $50, then the interest rate would be $50/$1000 = 5%.  Usually rates are stated in annual terms.  Requiring an extra $50 in interest after one year, on top of the repayment of the "principal" of the original $1000, is the equivalent of an interest rate of 5% per year.

If I agreed to loan you $1000 for an extra payment by you of $50, then the interest rate would be $50/$1000 = 5%.  Usually rates are stated in annual terms.  Requiring an extra $50 in interest after one year, on top of the repayment of the "principal" of the original $1000, is the equivalent of an interest rate of 5% per year.

The concept of "compounded interest" refers to earning interest on the interest.  "Compounded yearly" or "compounded annually" means that the interest is added to the total amount due at the end of the year, and then the interest for the next year is calculated by including the interest for the first year:

The concept of "compounded interest" refers to earning interest on the interest.  "Compounded yearly" or "compounded annually" means that the interest is added to the total amount due at the end of the year, and then the interest for the next year is calculated by including the interest for the first year.  Here is an example:

:*$1000 is loaned to you today at an interest rate of 5%, compounded annually.

:*$1000 is loaned to you today at an interest rate of 5%, compounded annually.

:*After one year, the amount due is $1000 plus 5% of $1000, for a total of $1050.

:*After one year, the amount due is $1000 plus 5% of $1000, for a total of $1050.

:*After two years, the amount due is $1050 plus 5% of $1050, for a total of $1102.50, because the interest on the first year is compounded in calculating the interest for the second year.

:*After two years, the amount due is $1050 plus 5% of $1050, for a total of $1102.50, because the interest on the first year is included in calculating the interest for the second year.

The opposite of "compounded" interest is "simple" interest.  In that case, the total about due the second is $1000 plus 5% of $1000 plus another 5% of $1000, for a total of $1100.  Notice how the total amount under compounded interest is always larger than the total amount using simple interest.

The opposite of "compounded" interest is "simple" interest.  In the above example, the total amount due the second year is $1000 plus 5% of $1000 (for the first year) plus another 5% of only the original $1000 (for the second year), for a total of $1100.  Notice how the total amount under compounded interest is always larger than the total amount using simple interest.

If you are saving money, then you want as much compounding of the interest as possible.  Ideally, you would like the interest on the money you save to be "compounded daily."

If you are saving money, then you want as much compounding of the interest as possible.  Ideally, you would like the interest on the money you save to be "compounded daily," such that each day's interest is on a total amount that includes all the interest that has accumulated for prior days.

Sometimes people repay money all at once, rather than with interest payments.  Suppose I gave you $1000 and you promised to pay me back $1500 in 10 years.  Then economists ask what is the “rate of return” or “yield” on that investment by me in your business?

Sometimes people repay money all at once, rather than with interest payments.  Suppose I gave you $1000 and you promised to pay me back $1500 in 10 years.  Then economists ask, what is the “rate of return” or “yield” on that investment?

That is more difficult to calculate.  I am receiving 50% return on my investment, but ten years from now.  At first glance, you may think to simply divide 50% by 10 years to calculate a rate of return of 5% per year.  That is a rough approximation, but not entirely precise.

That is more difficult to calculate.  I am receiving 50% return on my investment, but ten years from now.  At first glance, you may think to simply divide 50% by 10 years to calculate a rate of return of 5% per year.  That is a rough approximation, but not entirely precise.

What is wrong with it?  The flaw is that it fails to address the time value to money.

What is wrong with it?  The flaw is that it fails to address the time value to money.  We explain that next.

==The Time Value of Money==

==The Time Value of Money==