1. Money & Banking - ECO 473 - Dr. D. Foster
Interest Rates I:
The Basics
Money & Banking - ECO Dr. D. Foster

2. What is interest?
Payment made to savers to compensate them for foregoing consumption.
“The most powerful force in the universe is compound interest.”
Interest rates embody our expectations of the future.

3. What affects interest? Who cares?
Savers
Borrowers
Policymakers
Forecasters
Time value of money
Liquidity
Risk

4. Maturity date (in n years)
Interest Rates & Bonds
Bond $ $ $ $ $ $
$$$
mm/yyyy
Face value (FV)
Maturity date (in n years)
Coupons & value (C)
We will only consider annual coupons

5. i = nominal interest rate
Calculating Interest
Nominal yield: iN = C/F
Current yield: iC = C/P
Yield to maturity (YTM) interest return if bond held to maturity
aka, coupon yield
i = nominal interest rate

6. Present & Future Values
$1 today is worth more than $1 tomorrow
PV shows the “discounted” value of future $
$X in “n” years = $X/[(1+i)n] today
FV show the “compounded” value of present $
$X today = $X·(1+i)n in n years 6

7. $950 = $60/(1+i) + $60/[(1+i)2] + $60/[(1+i)3] + $1000/[(1+i)3]
Problems
You have $1000 now; i=5%, n=18. What is FV?
You get $1000 in 9 years; i=7%. What is PV?
You get $2000 in 4 years and $500 in 2 years; i=8%. What is the PV?
If the bond price is $950, the coupon is $60 and it matures in 3 years, what is its YTM?
1000*(1.0518) = $2406
1000/(1.079) = $544
2000/(1.084) + 500/(1.082) = $ $429 = $1899
Solve for i:
$950 = $60/(1+i) + $60/[(1+i)2] + $60/[(1+i)3] + $1000/[(1+i)3] 7

8. Interest Rates & Bond Pricing$ $ $ $ $ $
$$$
mm/yyyy
Face value (FV)
Maturity date (in n years)
Coupons & value (C)
Market price of the bond = present value of income stream discounted at the relevant market interest rate:
Special case: Perpetuity Price = C/i

9. Monetary policy  Bond Price will  interest rate
Fed buys bonds - price rises - interest rates fall - spending rises -  GDP
Fed sells bonds - price falls - interest rates rise - spending falls -  Inflation

10. Interest Rates, Bonds & the Fed$ $ $ $ $ $
$$$
mm/yyyy
Face value (FV)
Maturity date (in n years)
Coupons & value (C)
When the Fed buys bonds, their prices will ___ and interest rates will ___.
When the Fed sells bonds, their prices will ___ and interest rates will ___.

11. Quick Hits A wide spectrum of interest rates:
Federal Funds rate
Prime rate
30 year bond rate
Real interest rate (r)= i -  ( = inflation)
Note, this can only be calculated for past.
Note, i = re + e (e = expected values for r & )

12. Real and Nominal Interest Rates, 1980-2015
Nominal interest rate on 3 month Treasuries and real interest; derived as (3 month rate - CPI). 12

13. Bond Pricing Worksheet I
A bond has a face value (FV) of $1000, will mature in 2023 and has an annual coupon of $74 and the market rate of interest is 8.1%.
What is the current market price of this bond?
Suppose that interest rates change such that the current yield on this bond is 7.067%. What will be the market price for this bond? From this find the current market interest rate.
Suppose that when the bond was first sold, it’s market price was $ What must have been the market rate of interest then?
Consider a bond with FV=$1000, maturity = 2025, C=$81 and i=7.25%
What is the current price of this bond?
If the Fed jumps into the bond market, even though it just buys U.S. Treasuries, it will affect all interest rates to some extent. If they buy lots of bonds and interest rates fall to 6.88%, what will happen to the price of your bond?
The bond in #2 was given to you by your kindly aunt. She told you it matures in 2025, but her eyesight isn’t so good. You take a close look at the bond and see that it matures in Market i=7.25%.
What is the price of this bond? Why is it different than what you calculated in #2a?

14. Money & Banking - ECO 473 - Dr. D. Foster
Interest Rates I:
The Basics
Money & Banking - ECO Dr. D. Foster