1. Effective Annual Rates Nominal Rates Periodic Rates
Time Value of Money
Effective Annual Rates
Nominal Rates
Periodic Rates

2. We will deal with 3 different rates:
iNom = nominal, or stated, or
quoted, rate per year.
iPer = periodic rate.
EAR = EFF% =
effective annual
rate 29

3. iNom is stated in contracts. Periods per year (m) must also be given.
Examples:
8%; Quarterly
8%, Daily interest (365 days) 30

4. Periodic rate = iPer = iNom/m, where m is number of compounding periods per year. m = 4 for quarterly, 12 for monthly, and 360 or 365 for daily compounding.
Examples:
8% quarterly: iPer = 8%/4 = 2%.
8% daily (365): iPer = 8%/365 = %. 31

5. 6mo 12mo $1 Effective Annual Rate (EAR = EFF%):
Our bank offers a Certificate of Deposit (CD) with a 10% nominal rate, compounded semi-annually. What is the true rate of interest that they pay annually (the effective annual rate)?
6mo
12mo 5% 5% $1 32

6. How do we find EFF% for a nominal rate of 10%, compounded semiannually?
( )
iNom m
( ) 2
0.10 2 =
= (1.05)
= = 10.25%.
Any PV would grow to the same FV at 10.25% annually or 10% semiannually. 34

7. Financial Calculator
Using interest conversion:
2nd IConv
NOM%= 10 ENTER
C/Y = 2 ENTER
CPT EFF%= 10.25

8. EAR = EFF% of 10% EARAnnual = 10%. EARQ = (1 + 0.10/4)4 - 1 = 10.38%.
EARM = ( /12) = %.
EARD(365) = ( /365) = %. 35

9. Calculations using Excel (in edit mode, click on the insert below for Excel)

10. What is the FV of $100 after 3 years under 10% semiannual compounding?mn i æ ö FV = PV ç +
Nom ÷ n è ø m
2x3
0.10 æ ö FV =
$100 ç 1 + ÷ 3S è ø 2
= $100(1.05)6 = $ 40

11. Using a Financial Calculator
Using semi-annual periods:
INPUTS N
I/YR PV
PMT FV
OUTPUT
Using annual periods:
INPUTS N
I/YR PV
PMT FV
OUTPUT 40

12. Calculations using Excel (in edit mode, double click on the insert below for Excel)

13. What’s the value at the end of Year 3 of 3 $100 payments made at the end of each year. The quoted interest rate is 10%, compounded semiannually?
1yr
2yrs
3yrs 1 2 3 4 5
6 6-mos.
periods 5%
100
100
100 41

14. b. Use EAR = 10.25% as the annual rate in your calculator:
INPUTS N
I/YR PV
PMT FV
OUTPUT 46

15. Calculations using Excel (in edit mode, double click on the insert below for Excel)

16. Nominal, Periodic, or Effective Annual Rate?
We never use the nominal rate calculating future or present values. We always use either the effective annual rate or the periodic rate of return.
If PMT is 0, either the periodic rate or the effective rate may be used.
Ex: Find the present value of $100 to be received in 5 years. The nominal rate is 6 percent, compounded monthly. Periodic: FV = 100, N = 5*12, I = _______; compute PV= $ E.A.R.: FV = 100, N = 5, I = __________; compute PV= $74.14

17. If PMT has a value, N must equal the number of payments
If PMT has a value, N must equal the number of payments. Since N is determined by the number of payments, we must make I (the interest rate) consistent with how we defined N.
Ex: Find the present value of $100 per year for 5 years. The nominal rate is 6 percent, compounded monthly. PMT = 100, N = 5, I = _________; compute PV = $419.32
Ex: Find the present value of $100 per month for 5 years. The nominal rate is 6 percent, compounded monthly. PMT = 100, N = 5*12, I = ________; compute PV = $5,172.56

18. Evaluating the typical mortgage (in edit mode, double click on the insert below for Excel)

19. Amortization Schedule