Interest Rates
What is Interest?
Interest is the price that someone pays for the temporary use of someone else’s funds. To repay a loan, a borrower has to pay interest, as well as the principal, the amount originally borrowed.
Interest is the compensation that someone receives for temporarily giving up the ability to spend money. Without interest, lenders wouldn’t be willing to lend, or to temporarily give up the ability to spend, and savers would be less willing to defer spending.
Interest rates are expressed as percents per year. If the interest rate is 10 percent per year, and you borrow $100 for one year, you have to repay the $100 plus $10 in interest.
Because interest rates are expressed simply as percents per year, we can compare interest rates on different kinds of loans, and even interest rates in different countries that use different currencies (yen, dollar, etc.).
What are "APR" and "APY"?
"APR" stands for "Annual Percentage Rate," and "APY" for "Annual Percentage Yield."
The APR includes, as a percent of the principal, not only the interest that has to be paid on a loan, but also some other costs, particularly "points" on a mortgage loan.
Points (a point equals one percent of the mortgage loan amount) are fees that the mortgage lender charges for making the loan. In a sense, points are prepaid interest, or interest that is due when the loan is taken out.
Some lenders charge lower interest rates but more points than other lenders. The APR therefore provides a useful gauge for comparing the total cost of mortgage loans.
For example, a 30year mortgage with an interest rate of 8.0% and four points would have an APR of 8.44%, while a mortgage with an interest rate of 8.25% and one point would have an APR of 8.36%.
The principal used in calculating the
APR is equal to the amount of the loan the borrower
actually has to use at any time. Consider two oneyear
loans of $1,000, each with an interest rate of 10%,
or $100 in interest. 

6 Months 
12 Months 
LOAN #1: 
$1,000 LOAN 

Repay $1,000
Plus $100 Interest 
LOAN #2: 
$1,000 LOAN 
Repay $500
Plus $50
Interest 
Repay $500
Plus $50
Interest 

The second loan has a higher APR,
even though the amount of interest paid ($100)
is the same on both loans. The second loan has
a higher APR because the second borrower, unlike
the first borrower, does not have the use of the
entire $1,000 for the entire year, because the
second borrower repaid $500 of the loan after
six months. (Another reason the second loan has
a higher APR is that the borrower paid half of
the interest after six months and half at the
end of the year, rather than all the interest
at the end of the year.) 
"APY" is the effective interest rate from the standpoint of a person receiving interest. If you have $1,000 in each of two bank accounts, each paying the same interest rate, but the interest is credited more often (let’s say, every month, rather than once a year) on one of the accounts, that account will have a higher APY, because the interest will build up more rapidly than on the other account.
Why Does Interest Exist?
From the lender’s point of view:

Interest compensates lenders for the effects of inflation, or rising prices. Prices go up every year, so lenders are repaid with dollars that can’t buy as much as the dollars they lent; the lenders must be compensated for that loss of purchasing power.

Interest also compensates lenders for the risks they take. One risk is that nobody knows for certain how much prices will go up during the time that the borrower has the lender’s money. Other risks are that the borrower won’t repay the loan fully, on time, or at all.

For a lender such as a bank, interest covers the costs of staying in business, including the cost of processing loans, and interest also provides the profit that a lender needs to stay in business.
From the borrower’s point of view:

Individuals are willing to pay interest to borrow money in order to be able to spend now, rather than later, on cars and many other items.

Individuals are willing to pay interest in order to be able to afford a large purchase, such as a home, for which they don’t have enough funds of their own.

Individuals are willing to pay interest on loans to pay for education, which can increase their earning ability.

Businesses are willing to pay interest in order to borrow to invest in equipment, buildings, and inventories that will increase their profits.

Some borrowers are willing to pay interest on certain loans because of the associated tax advantages. Mortgage interest, for example, is tax deductible. That means that in calculating how much income tax you have to pay, you can subtract the mortgage interest that you pay from your income.

Banks are willing to pay interest on their customers’ deposits because they can lend the funds at higher interest rates and make a profit.
Interest:
Cost to Some, Income to Others?
Interest is income to people willing to give up the temporary use of their money. When you put money into a bank account, or when you buy a U.S. Savings Bond, for example, you receive interest income.
Interest is a cost to borrowers. You pay interest, for example, if you don’t pay your entire credit card bill at the end of the month, if you take out a mortgage loan to buy a house, or if you own a business that borrows in order to invest in machinery.
Interest is a signal that directs funds to where they can earn the highest rates, or to where loans can do the most for the economy.
Interest is a measure of the cost of holding money. The rate of interest that you could earn by lending your money is the cost to you of holding your money in a way (such as in cash) that doesn’t earn any interest. Economists use the term "opportunity cost" to refer to what you give up by choosing a certain course of action. By holding money, you give up the interest that you could have earned, so the interest rate measures the opportunity cost of holding money.
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