Option Trading Lesson 1.5

What Is an Interest Rate?

• The interest rate is the amount charged on top of the principal by a lender to a borrower for the use of assets.
• Consumer loans typically use an APR, which does not use compound interest.

When the borrower is considered to be low risk by the lender, the borrower will usually be charged a lower interest rate. 

If the borrower is considered high risk, the interest rate that they are charged will be higher, which results in a higher cost loan.

Annual percentage rate (APR) 

The annual rate charged for borrowing or earned through an investment. APR is expressed as a percentage that represents the actual yearly cost of funds over the term of a loan or income earned on an investment. 

Annual percentage yield (APY) 

The actual rate of return that will be earned in one year if the interest is compounded, simply the % of growth in an investment over a specific period of time.

• Compound interest is added periodically to the total invested, increasing the balance. That means each interest payment will be larger, based on the higher balance.
• The more often interest is compounded, the better the return will be.

The formula for calculating APY is:

APY= (1 + r/n )n – 1

Where:

• r = period rate 
• n = number of compounding periods

For example, if you deposited $100 for one year at 5% interest and your deposit was compounded quarterly, at the end of the year you would have $105.09. If you had been paid simple interest, you would have had $105.

The APY would be (1 + .05/4)4 - 1 = .05095 = 5.095%.

It pays 5% a year interest compounded quarterly, and that adds up to 5.095%. That's not too dramatic. However, if you left that $100 for four years and it was being compounded quarterly then the amount your initial deposit would have grown to $121.99. Without compounding it would have been $120.

X = D(1 + r/n)^n*y

= $100(1 + .05/4)^4*4

= $100(1.21989)

= $121.99

where:

• X = Final amount
• D = Initial Deposit
• r = period rate 
• n = number of compounding periods per year
• y = number of years

How Can APY Assist an Investor?

Any investment is ultimately judged by its rate of return, whether it's a certificate of deposit, a share of stock, or a government bond. 

What Is the Difference Between APY and APR?

APY and APR are both standardized measures of interest rates expressed as an annualized percentage rate.

APY takes into account compound interest while APR does not. Furthermore, the equation for APY does not incorporate account fees, only compounding periods. That's an important consideration for an investor, who must consider any fees that will be subtracted from an investment's overall return.

Source: Investopedia