Download - Mod 6 - Ir - Apr and Ear
7/14/2015
1
Michael R. Roberts
William H. Lawrence Professor of Finance
The Wharton School, University of Pennsylvania
Interest Rates:APR and EAR
Copyright © Michael R. Roberts
Copyright © Michael R. Roberts
Last TimeTime Value of Money• Intuition, tools and discounting• Compounding• Useful shortcuts• Taxes• Inflation
7/14/2015
2
Copyright © Michael R. Roberts
This TimeInterest Rates• Interest rate quotes• Non-annual cash flows and
compounding
APR & EAR
Copyright © Michael R. Roberts
7/14/2015
3
Current 5-Year Jumbo CD Rates
*Bankrate.com as of 12/16/2014
Copyright © Michael R. Roberts
Current 5-Year Jumbo CD Rates
*Bankrate.com as of 12/16/2014
Difference between “Rate” and “APY”?
Copyright © Michael R. Roberts
7/14/2015
4
Current 5-Year Jumbo CD Rates
*Bankrate.com as of 12/16/2014
Rate = APR or Annual Percentage Rate
Copyright © Michael R. Roberts
Current 5-Year Jumbo CD Rates
*Bankrate.com as of 12/16/2014
Rate = APR or Annual Percentage Rate
Measures amount of simple interest earned in a year
Copyright © Michael R. Roberts
7/14/2015
5
Current 5-Year Jumbo CD Rates
*Bankrate.com as of 12/16/2014
Rate = APR or Annual Percentage Rate
Simple interest = interest earned without compounding
Copyright © Michael R. Roberts
Current 5-Year Jumbo CD Rates
*Bankrate.com as of 12/16/2014
Rate = APR or Annual Percentage Rate
Many bank quotes are in terms of APR
Copyright © Michael R. Roberts
7/14/2015
6
Current 5-Year Jumbo CD Rates
*Bankrate.com as of 12/16/2014
Rate = APR or Annual Percentage Rate
APR typically not what we earn or pay
Copyright © Michael R. Roberts
Current 5-Year Jumbo CD Rates
*Bankrate.com as of 12/16/2014
APY = Annual Percentage Yield
Copyright © Michael R. Roberts
7/14/2015
7
Current 5-Year Jumbo CD Rates
*Bankrate.com as of 12/16/2014
APY = EAR or Effective Annual Rate
Copyright © Michael R. Roberts
Current 5-Year Jumbo CD Rates
*Bankrate.com as of 12/16/2014
APY = EAR or Effective Annual Rate
EAR measures actual amount of interest earned/paid in year
Copyright © Michael R. Roberts
7/14/2015
8
HOW ARE DIFFERENT RATES RELATED?
Copyright © Michael R. Roberts
Lesson: EAR is a discount rate
EAR is what matters for computinginterest and discounting cash flows
Copyright © Michael R. Roberts
7/14/2015
9
Lesson: APR is not a discount rate.
APR is a means to an end. We use itto get a discount rate (e.g., EAR)
Copyright © Michael R. Roberts
How do we get from an APR to an EAR (and vice versa)?
Copyright © Michael R. Roberts
7/14/2015
10
Lesson: The relation between APRand EAR is:
Copyright © Michael R. Roberts
k is the number of compounding periods
per year
Lesson: The relation between APRand EAR is:
Copyright © Michael R. Roberts
7/14/2015
11
i is the periodic interest rate, orperiodic discount rate
Lesson: The relation between APRand EAR is:
Copyright © Michael R. Roberts
Example
• Invest $100 in CD offering 5% APR with semi-annual compounding. How much money will you have in one year?
Copyright © Michael R. Roberts
7/14/2015
12
Example
• Invest $100 in CD offering 5% APR with semi-annual compounding. How much money will you have in one year?
0 ?
?100
Period
Copyright © Michael R. Roberts
Example
• Invest $100 in CD offering 5% APR with semi-annual compounding. How much money will you have in one year?
0
?100
2Period
k = 2
Copyright © Michael R. Roberts
7/14/2015
13
Example
• Invest $100 in CD offering 5% APR with semi-annual compounding. How much money will you have in one year?
0
?100
2Period
Period 1 (n = 1)
1
Period 2 (n = 2)
Copyright © Michael R. Roberts
Example
• Invest $100 in CD offering 5% APR with semi-annual compounding. How much money will you have in one year?
0
?100
2Period
1
Copyright © Michael R. Roberts
7/14/2015
14
Example
• Invest $100 in CD offering 5% APR with semi-annual compounding. How much money will you have in one year?
0
?100
2Period
1
Earn 2.5% interest Earn 2.5% interest
Copyright © Michael R. Roberts
Example
• Invest $100 in CD offering 5% APR with semi-annual compounding. How much money will you have in one year?
0
?100
2Period
1
100 x (1+0.025)1102.5
Copyright © Michael R. Roberts
7/14/2015
15
Example
• Invest $100 in CD offering 5% APR with semi-annual compounding. How much money will you have in one year?
0
100
2Period
1
100 x (1+0.025)1102.5
102.5 x (1+0.025)1105.0625
Copyright © Michael R. Roberts
Example
• Invest $100 in CD offering 5% APR with semi-annual compounding. How much money will you have in one year?
0
100
2Period
1
100 x (1+0.025)1102.5
102.5 x (1+0.025)1105.0625
Copyright © Michael R. Roberts
7/14/2015
16
Example
• Invest $100 in CD offering 5% APR with semi-annual compounding. How much money will you have in one year?
0
100
1Year
?
Copyright © Michael R. Roberts
Example
• Invest $100 in CD offering 5% APR with semi-annual compounding. How much money will you have in one year?
0
100
1Year
0.5
?
Copyright © Michael R. Roberts
7/14/2015
17
Example
• Invest $100 in CD offering 5% APR with semi-annual compounding. How much money will you have in one year?
0
100
1Year
0.5
?
Copyright © Michael R. Roberts
Example
• Invest $100 in CD offering 5% APR with semi-annual compounding. How much money will you have in one year?
0
100
1Year
0.5
105.0625
Earn 5.0625% interest
Copyright © Michael R. Roberts
7/14/2015
18
Example
• Invest $100 in CD offering 5% APR with semi-annual compounding. How much money will you have in one year?
0
100
1Year
0.5
105.0625
Earn 5.0625% interest
Copyright © Michael R. Roberts
Lesson: If you discount cash flowsusing EAR, then measure time inyears. If you discount cash flows usingperiodic interest rate, then measuretime in periods.
Copyright © Michael R. Roberts
7/14/2015
19
Proof
where N = kT = # of periods
Copyright © Michael R. Roberts
Periods vs Years
0 2
105.0625100
1
100 x (1+0.025)102.5
102.5 x (1+0.025)
Periods
Copyright © Michael R. Roberts
7/14/2015
20
Periods vs Years
0 1
105.0625100
0.5
100 x (1+0.050625)1/2102.5
102.5 x (1+0.050625)1/2
0 2
105.0625100
1
100 x (1+0.025)102.5
102.5 x (1+0.025)
Periods
Years
Copyright © Michael R. Roberts
Current 5-Year Jumbo CD Rates
*Bankrate.com as of 12/16/2014
APR = 2.37%
Copyright © Michael R. Roberts
7/14/2015
21
Current 5-Year Jumbo CD Rates
*Bankrate.com as of 12/16/2014
APR = 2.37%k = 365 (or 360, 252)
Copyright © Michael R. Roberts
Current 5-Year Jumbo CD Rates
*Bankrate.com as of 12/16/2014
APR = 2.37%k = 365 (or 360, 252)
i = 2.37% / 365= 0.006714%
Copyright © Michael R. Roberts
7/14/2015
22
Current 5-Year Jumbo CD Rates
*Bankrate.com as of 12/16/2014
APR = 2.37%k = 365 (or 360, 252)
i = 2.37% / 365= 0.006714%
EAR = (1+0.006714%)365-1= 2.398%
Copyright © Michael R. Roberts
Summary
Copyright © Michael R. Roberts
7/14/2015
23
Lessons
• EAR is a discount rate– Measures cash flows in years
• Period interest rate, i, is a discount rate– Measures cash flows in periods
• APR is not a discount rate
Copyright © Michael R. Roberts
Lessons
• Moving between EAR and APR
where
i = APR / k and k = # of periods per year
Copyright © Michael R. Roberts
7/14/2015
24
Coming up next
• Interest Rates– Term Structure of interest rates and the
yield curve
Copyright © Michael R. Roberts