What is "Interest"?
Interest:
 It's expressed as an annual percentage rate

Cost of the use of money.
 It may be fixed. variable, or a combination
 Fixed= doesn't change over life of term
 Variable= % rate ca n change over life of intrument. Changes usually occur related to macroeconomic rate such as Fed or prime rate.
 Changing bases= rate type may change from: fixed to variable or variable to fixed over life of instrument.
What is "Stated Interest Rate"?
Stated Interest Rate: (sometimes referred to as nominal interest rate) is the annual rate of interest specified (stated) in a contract.
 Examples:
 Rate per loan agreement
 Bond coupon rate
 It does not take into account compounding effects of frequency of payments.
 Assume:
 Semiannual interest
 Stated rate=6%
 Effective rate>6% due to frequency of payments (onehalf of the interest is paid before end of year.
 Stated rate still 6%
Define "Simple Interest":
Simple Interest: Interest computed on original principal only.
 No compounding in interest calculation
 No interest paid on interest
Example:
 2 yr, $2,000 note @ 6% with simple interest paid at end of borrowing period.
 Interest= Principal x Rate x Time
 Interest+ $2,000x.06x2yrs= $240
 No interest paid on 1st year's interest.
Define "Compound Interest":
Compound Interest: Interest computed on principal plus accumulated unpaid interest.
 Interest is paid on interest.
Example:
 2 yr, $2,000 note @ 6% compounded annually, but paid at end of borrowing period.
 Interest Yr1: $2,000x.06x1 = $120
 Interest Yr2: $2,000+120=$2,120x.06x1= $127.20
 Total interest = $247.20

FV method:
 FV= P(1+i)^n;
 P=Orig Principal, i=int rate, n=# of periods
 FV=$2,000(1+.06)^2
 FV=$2,247.20
Define: Effective Interest Rate:
Effective Interest Rate: Annual interest rate implicit in the relationship between the net proceeds of a borrowing and the dollar cost of that borrowing.
 Calculation: Net cost of borrowing (interest paid) / Net proceeds.
 Net proceeds received may be less than amount borrowed due to:
 Discountinginterest deducted in advance
 Compensating balance requirement

Example:
 $2,000, 2 yr note discounted @ 6%
 Discounted= Interest deducted in advance
 Simple Interest= $2,000x.06x2= $240
 Net proceeds= $2,000240= $1,760
 Effective interest=($240/$1,760)/2yrs
 = 13.64/2 = 6.82%
 Effective Interest Rate = 6.82%
What is the "Annual Percentage Rate"? (APR)
Annual Percentage Rate: Annualized effective interest without compounding on a borrowing that is for a fraction of a year.
 Computed: APR= Effective rate for fraction of year x # of fractions in year
 Fractions:
 Semiannual = 2
 Quarterly = 4

Example:
 $2,000, 90 day note discounted @6%
 Simple Int = $2,000x.06x(90/360)= $30
 Effective Int= $30/$1,970=1.52% for 90 days (quarter)
 APR= 1.52x4 quarters = 6.08%
 $2,000, 90 day note discounted @6%
 APR is the legally required basis for interest rate disclosure in US.
What is "Effective Annual Percentage Rate"? (EAPR)
Effective Annual Percentage Rate: Annualized effective interest with compounding on a borrowing that is for a fraction of a year.
 Also called "Annual Percentage Yield
 Formula: EAPR= (1 + I/p)^p  1
 Where:
 I= Annual stated rate
 p=# of periods in a year
 Example:
 $2,000, 90 day note @6%
 Calculation:
 EAPR: (1 + .(06/4))^4  1
 EAPR: .06136>.06 stated rate
What is "Real Interest Rate"?
Real Interest Rate = Nominal interest rate  Inflation rate
Question:
Which one of the following is the annual rate of interest applicable when not taking trade credit terms of "2/10, net 30?"
A. 2.00% B. 24.00% C. 36.00% D. 36.73%
36.73%
Credit terms of "2/10, net 30" mean that the debtor may take a 2% discount from the amount owed if payment is made within 10 days of the bill, otherwise the full amount is due within 30 days. The 2% discount is the interest rate for the period between the 10th day and the 30th day; it is not the effective annual rate of interest. The computation of the annual rate of interest using $1.00 would be:
Interest 1
APR = _______ x ________________
Principal Time fraction of year
.02 1
APR = ___ x ______ = .0204 x (360/20) =
.98 20/360
APR = .0204 x 18 = 36.73%
Thus, the effective annual interest rate for not taking the 2% (.02) discount is 36.73%. The 20 days in the 360/20 fraction is (30  10), the period of time over which the discount was lost as a result of not paying early.
The following information is available on market interest rates:
The riskfree rate of interest 2%
Inflation premium 1%
Default risk premium 3%
Liquidity premium 2%
Maturity risk premium 1%
What is the market rate of interest on a oneyear U.S. Treasury bill?
3%
The market rate of interest on a oneyear U.S. Treasury bill would be 3%. Notice that the riskfree rate of interest and the various premiums are for the general market rate of interest, not for the rate on a oneyear U.S. Treasury bill. Treasury bills are considered risk free in an environment where zero inflation is expected. Therefore, the market rate of interest on a oneyear U.S. Treasury bill would be the riskfree rate plus the inflation premium (for the expected rate of inflation during the life of the security), or 2% + 1% = 3%. Oneyear U.S. Treasury bills are considered free of default risk, liquidity risk (because there is a very large and active secondary market for Tbills), and maturity risk (because they are for only one year).