What is an APR?
An interest rate is a rate which is charged or paid for the use of money. An interest rate is often expressed as an annual percentage of the principal. It is calculated by dividing the amount of interest by the amount of principal. APR is defined as the yearly cost of a mortgage, including interest, mortgage insurance, and the origination fee (points), expressed as a percentage.
Let’s first examine the definition for interest rate. Simply put, it’s a rate that the borrower pays for using the lender’s money. Just like you would pay to rent a car or a punch bowl for a wedding, you pay to rent money.
Interest is typically stated in a percent of the amount owed that’s due every year of the loan. A real simple example would be if you borrowed $100 from a friend and agreed to pay him/her back one year from today along with 8% interest. When the year was up you would need to give your friend $108 (the original $100 plus $8 interest).
So, how does the frequency of compounding effect the real cost of borrowing? In our example, the interest was compounded once a year. But what would happen if we compounded it twice a year? At the end of the year, You would need to pay your friend $108.16.
Why sixteen cents more than the original example? You’d still have to pay back the same $100 principal, but because the interest is compounded twice each year, you’d need to calculate and add two separate interest payments. For the first six months, You’d owe $4 ($100 principal multiplied by 8% annual interest divided by two equals 4%).
But for the next six months, you’d owe $4.16. Because interest was owed (and unpaid) after the first six months, the principal amount was increased by $4 to $104. And 4% (half of 8%) of $104 is $4.16. So over the entire year, you’d owe $8.16 for interest ($4 first six months plus $4.16 for the second six months).
If we were to compound daily, the total due at the end of a year would be $108.33. So even though the interest rate stays the same (8%), the amount that you’ll pay could vary by $0.33 depending on how often interest is compounded. Not a tremendous amount, but it does add up when you’re borrowing hundreds of thousands of dollars.
The APR will include any additional costs caused by frequent compounding. When it’s used in a mortgage situation, it also includes mortgage insurance and any “points” that came with the mortgage. For most of us, it’s almost impossible to calculate how much we’d owe on a mortgage with all the different variables involved. The APR does that for us. We can take two mortgages and compare the APR on each. You can also use the APR to compare non-mortgage consumer loans.
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