Q1:() The current price of a $1,000 par 20-year zero-coupon bond is $204. What i
ID: 2819456 • Letter: Q
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Q1:() The current price of a $1,000 par 20-year zero-coupon bond is $204. What is the bonds implied yield (rate of interest)? (6) a. b. c. If continuous compounding is used (3) If semi-annual compounding is used (3) If annual compounding is used (3) Q2: (6) Suppose a lender quotes the interest rate on a $1,000 loan as 9.0% per annum with continuous compounding but the interest is actually paid monthly. What are the monthly interest payments? (6) Assume the following continuously compounded zero rates: 1.0% at 0.5 years 1.6% at 1.0 year; 1.9% at 1.5 years, and 2.5% at 2.0 years (that is, it costs 1.0% annually with continuous compounding to borrow money for 0.5 years, it costs 1.6% annually with continuous compounding to borrow money for 1.0 years, it costs 1.9% annually with continuous compounding to borrow money for 1.5 years and it costs 2.5% annually with continuous compounding to borrow money for 2.0 years). What is the theoretical price of a bond with a $100 principal that pays coupons at the rate of 2.0% semiannually? (i.e. the bond pays $1 at 0.5 years, $1 at 1.0 years, $1 at 1.5 years and $101 at 2.0 years) (5) Q3: (5) Q4: (5) Assume the following theoretical continuously compounded spot rates: 20% at 0.5 years; 30% at 1.0 year; 4.0% at 1.5 years, and 5.0% at 2.0 years. What is the two-year PAR YIELD with continuous compounding? (The PAR yield is the coupon yield when makes the bond price equal to its face value or principal, e.g. for a $100 face value bond it is the coupon rate that makes the price of the bond- $100). (5)Explanation / Answer
Continuously Compounding Semi-annual Compounding Annual Compounding Face Value $1,000.00 $1,000.00 $1,000.00 Coupon Rate 0.00% 0.00% 0.00% Period 20 40 20 Present Vale $204.00 $204.00 $204.00 YTM = Rate(20,0,-204,1000) 8.27% 4.05% 8.27% Annual Interest Rate 8.27% 8.11% 8.27% Continuously Compounding FV= P e^r $1000 = $204 Exp(r) Exp(r) = 1000/204 8.27% Semiannual compounding = 2 x 4.05% 8.11%
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