1. Interest Rates
Interest rates play a leading role in a majority of financial productions, especially when discussing bonds, credit cards, loans and mortgages. However, in today’s lesson, we’ll not only define interest rates, but discuss the difference between real interest rates, rates adjusted for inflation, and nominal interest rates, which are not.

2. Interest Rates Cont’d
Let’s start by exploring interest rates in relation to a simple loan and present value.
When one acquires a simple loan, the lender (banking institutions) provides the borrower with funds that must be repaid by a maturity date along with interest.
Present value, a component of a simple loan, is based on the notion that the dollar ($) paid one from now is less valuable than the dollar paid today.

3. Interest Rates Continued
Example: Your friend Michelle borrowed $100 from you with the expectation that she will repay you in 1 year, at an interest rate of $10. How much will Michelle owe you after one year? If you loathe math, it is ok to cringe.
First, determine interest rate: i= interest rates, therefore i= $10 (interest)/$100 (given value) = .10 or 10%
Next, plug the found interest rate into the following equation: $100 x (1 + interest rate) = $100 x (1+ .10)= $100 x (1.10)= $110
Therefore, you are content lending Michelle $100 today, just as you will be content receiving $110 a year from now.
The above equation is an example of discounting the future where we calculated today’s value of dollars expected to be received in the future.

4. Interest Rates Cont’d Now let’s explore present value.
Example: What is the present value of $250 to be repaid in two years if the interest rate is 15%?
We can start with a key:
CF= cash flow in two years = 250
i= annual interest rate = . 15 (15/100)
n= number of years = 2
Thus, the formula is as follows: PV= CF/(1 + i) ^n
So, PV= $250/( ) ^2 = $250/1.3225= $189.04

5. Interest Rates Cont’d
As we can see, the dollar amount in the future, $189.04, is less valuable than the present amount of $250.
Let’s continue by examining the array of credit market institutions and additional loans.
The first is the simple loan previously discussed. As a reminder, this is a loan for which a lender provides the borrower with funds that must be repaid at a maturity date plus interest.
The second is a fixed-payment loan, where the lender provides the borrower with an amount of funds, which must be repaid in a fixed amount of time.

6. Interest Rated Cont’d In addition to loans, we have coupon bonds.
A coupon bond pays the owner of the bond a fixed interest payment every year, until the maturity date and the specified final amount is paid.
Example: A coupon bond with $1,000 face value might pay you a coupon payment of $100 per year for 10 years, and after 10 years you repay the amount of $1,000.
Finally, we have discount bonds, which are bought at a price below the face value and the face value is repaid at the maturity date.
Unlike a coupon bond, there is no interest paid in a discount bond.

7. Interest Rates Cont’d
Moreover, for a coupon bond, there are interesting facts that emerge:
When a coupon bond is priced at face value, the yield to maturity equals the coupon rate.
The price of the coupon rate and the yield to maturity are negatively related -- when YTM increases, the price of the bond falls.
YTM is greater than (>) coupon rate when the bond price is less than (<) face value.
The word yield to maturity has frequently appeared in this presentation and as such, it is the interest rate that parallels the present value of cash flow payments with its value today.
Example: If John borrows $100 from his sister and she expects $110 from him in return next year, what is the yield to maturity on this loan?

8. Interest Rates Cont’d The formula is as follows:
PV = CF/(1 + i) ^n = $100 = $110/(1 + i)
When you cross multiply, you get (1 + i) $100 = $110.
Then, you divide both sides by $100 and you have (1 + i) = $110/$100 which equals 1+i = 1.10.
Finally, you solve for i, you get i = = .10 or 10%
Rule: For simple loans, the simple interest rate equals the yield to maturity.
As we move forward in our lesson, let’s explore the confusion between interest rates and rates of return.
As such rates of return are the payments to the owner plus the change in its value which is a fraction of the purchase price.

9. Interest Rates Cont’d
Thus, the return on a bond will not necessarily equal the yield to maturity on that bond.
Next, let’s analyze the relationship between interest rates and bonds:
When the maturity date is the same as the holding period, then the bond’s return equals the full year to maturity (YTM).
A rise in interest rates will make a bond’s price fall.
The more distant a bond’s maturity, the greater (>) the percentage price associated with interest rate.
As a result of this great distance, the rate of return will be lower.
Let us now turn our attention to inflation.
In studying inflation and its effects, we have to comprehend nominal interest rate and real interest rate.

10. Interest Rates Cont’d
Nominal interest rate is defined as real rate + expected rate of inflation.
Real interest rate is defined as nominal interest rate – expected rate of inflation.
When the real interest rate is low, there are greater incentives to borrow and fewer incentives to lend.
The difference between nominal and real interest rates is important because it reflects the real cost of borrowing.