Financial Management: Interest Rate Concepts and Calculations Flashcards Preview

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Flashcards in Financial Management: Interest Rate Concepts and Calculations Deck (10):
1

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. 

2

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%

 

3

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.

4

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 

5

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%

6

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%
  • APR is the legally required basis for interest rate disclosure in US.

7

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

8

What is "Real Interest Rate"?

Real Interest Rate = Nominal interest rate - Inflation rate

9

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.

10

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).