# Interest Rates I: Money & Banking - ECO 473 - Dr. D. Foster - PowerPoint Presentation

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

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.

What affects interest? Who cares? Time value of moneyLiquidity Risk Savers Borrowers Policymakers Forecasters

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

Calculating Interest Nominal yield: i N = C/FCurrent yield: i C = C/PYield to maturity (YTM) . . . interest return if bond held to maturity i = nominal interest rate aka, coupon yield

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

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? Problems 1000*(1.05 18 ) = \$2406 1000/(1.07 9 ) = \$544 2000/(1.08 4 ) + 500/(1.08 2 ) = \$1470 + \$429 = \$1899 \$950 = \$60/(1+i) + \$60 /[(1+i) 2 ] + \$60 /[(1+i)3] + \$1000 /[(1+i)3] Solve for i:

Interest Rates & Bond Pricing Face value (FV) \$\$\$ mm/yyyy \$ \$ \$ \$ \$ \$ Bond 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

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

Interest Rates, Bonds & the Fed Face value (FV) \$\$\$ mm/yyyy \$ \$ \$ \$ \$ \$ Bond 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 ___.

Quick Hits A wide spectrum of interest rates:Federal Funds rate Prime rate30 year bond rateReal interest rate (r)= i -  ( = inflation)Note, this can only be calculated for past.Note, i = r e +  e (e = expected values for r & )

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

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 \$1000. 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 2021. Market i=7.25%.What is the price of this bond? Why is it different than what you calculated in #2a?

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

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