Financial Management: Interest Rate Concepts and Calculations Flashcards
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 macro-economic 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:
- Semi-annual interest
- Stated rate=6%
- Effective rate>6% due to frequency of payments (one-half 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:
- Discounting-interest 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= $2,000-240= $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:
- Semi-annual = 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 risk-free 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 one-year U.S. Treasury bill?
3%
The market rate of interest on a one-year U.S. Treasury bill would be 3%. Notice that the risk-free rate of interest and the various premiums are for the general market rate of interest, not for the rate on a one-year 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 one-year U.S. Treasury bill would be the risk-free rate plus the inflation premium (for the expected rate of inflation during the life of the security), or 2% + 1% = 3%. One-year U.S. Treasury bills are considered free of default risk, liquidity risk (because there is a very large and active secondary market for T-bills), and maturity risk (because they are for only one year).
