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

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

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

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

Present & Future Values 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 5

$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 Verify this answer. $1899 $950 = $60/(1+i) + $60/[(1+i)2] + $60/[(1+i)3] + $1000/[(1+i)3] 6

Interest Rates, Bond Pricing & 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 ___.

Bond Pricing Worksheet I A bond has a face value (FV) of $1000, will mature in 2024 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 = 2026, 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 2026, but her eyesight isn’t so good. You take a close look at the bond and see that it matures in 2022. Market i=7.25%. What is the price of this bond? Why is it different than what you calculated in #2a?

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