FIN 614: Financial Management
Larry Schrenk, Instructor
1. What is an Interest Rate?
2. Types of Interest Rates
3. Conversions between Types of Interest
Rates
Compensation for the Lending of
Money
Loss of the Use of an Asset
Stated in Percentage Terms (Relative to
the Principal)
Similar to a Rental or Leasing Charge
Holding Period Return, HPR
Annual Percentage Rate, APR, NOM%
Period Rates, rmonthly, rquarterly, etc.
Effective (or Equivalent) Annual Rate,
EAR, EFF%
Most Basic Rate Calculation
Change from one point of time (t = 0) to
another (t = 1):
V1  V0
HPR 
V0
HPR = Holding Period Return
V1 = Value at t = 1
V0 = Value at t = 0
NOTE: The time from t0 to t1 need not be a year.
My portfolio was worth $123,000 5 years
ago and it is now worth $131,000:
131,000  123,000
HPR 
 0.065  6.5%
123,000
REMEMBER: The earlier value always goes in the denominator!
Problem: Comparing assets with different
holding periods.
Which is better?
7.8% over 7 years
10.5% over 10 year
Need a common time period
Convert all rates to an annual basis
‘Annualize’ them
Annual Cost of Borrowing Including Fees
and Transaction Costs
Legal Standard–Consumer Credit
Protection Act (1968)
Does not Incorporate Compound
Interest
Formula:
APR  ri  m
APR = Annual Percentage Rate
ri = Return for Period i
m = Periods per Year
What is my APR is my weekly return is
0.25%?
rweekly x m = 0.25% x 52 = 13.00%
APR = 13.00%
Period Rate is the Rate over a Certain
Period
It is the HPR for the Period
If your stock was at $110 at the end of
last month and $108 at the end of this
month:
HPRmonthly  rmonthly
108  110

 0.0181  1.81%
110
EAR Incorporates Compound Interest
Accurate Calculation of Return
Formula:
EAR  1  ri   1
m
EAR = Effective Annual Return
ri = Return for Period i
m = Periods per Year
If your monthly return is 2%, what is your
EAR?
EAR  1.02   1  26.82%
12
EAR → APR
1


m
APR    EAR  1  1 m


EAR = Effective Annual Return
APR = Annual Percentage Rate
m = Periods per Year (for APR)
APR → EAR
m
APR 

EAR   1 
1

m 

Also, a calculator function is available.
If you get 1% return each month:
EAR  1.01  1  12.68%
12
APR  0.01 12  12.00%
If I invested $1.00, I would have $12.68.
EAR accurately calculates the actual
return.
ARP underestimates your return, since it
does not incorporate compound interest.
My investment portfiolo increased from
$125,500 to $275,100 in 5 years, find my EAR?
N=5
I%=0 ◄ Select I%, then [ALPHA] [ENTER]
PV=-125500
PMT=0
FV=275100
P/Y=1
C/Y=1
PMT: END BEGIN
I% = 17.00%
1. [ON]
2. [APPS] [ENTER]
3. CALC
VARS
1: TVM Solver...
2: tvm_Pmt
3: tvm_I%
4: tvm_PV
5: tvm_N
6: tvm_FV
7↓npv(
4. Scroll Down to ‘B:►Nom(’ or ‘C:►Eff(’ ENTER
NOTE: EAR = (Eff)ective Rate and APR = (Nom)inal Rate
►Nom( Function
Syntax: ►Nom(EAR, m)
What is the APR (Nom) based on
quarterly periods, if the EAR (Eff) is 13%?
►Nom(13, 4
APR = 12.41%
ENTER
►Eff( Function
Syntax: ►Eff(APR, m)
What is the EAR (Eff), if the APR (Nom)
based on weekly periods is 15%?
►Eff(15, 52
EAR = 16.16%
ENTER
FIN 614: Financial Management
Larry Schrenk, Instructor