Why are we using both PV Ordinary annuity and PV single amount, and adding them together to answer this question?

Question: What would you pay for a GM 9.5 that matures in 10 years if the yield (prevailing rate) on similar risk bonds issued today is 10.5%?

1. Look at dollar returns 2. Look at the value of those returns today - adjusted for risk Series of equal payment at equal intervals Annuity! Coupon =0.095 x $1,000 Intervals = 6 months Use this to figure out n rould you pay for a GM 9.5 that matures in a 10 years if the yield (prevailing rate) on similar risk bonds issued today is 10.5%? Expected RETURN Anything else we receive with this investment? Face value = $1,000 2. Draw timeline. What are we calculating? Today 1 2 10 ? $47.50 $47.50 $47.50 $47.50 $$ $47.50 $1,000 PMT (annuity) =$95/2 FV (single amounty=$1,000 PVdeamount +PV ordinary annuity single 3. What is my "" and "n"? - we need to discount using TODAY'S prevailing interest rates (in this case, the yield on similarly risky bonds) therefore we will use the discount rate of 10.5% interest and payments happen at same frequency (2 times per year) Note: yield can be assumed to be compounded semi-annually if not explicitly stated r=. 105/2 =.0525 n =10 x 2 = 20 4. PLUG NUMBERS INTO FORMULAS PMT (annuity) =$47.50 FV(single amount) $1,000 r.0525 n=20 PVs+ PVA (1-(1+r)"] PVOX - PMT FV PV= (1+r)" 1,000 (1.0525) PVs4 = $359.3833 PVSA PV4-47.50 1-(1+0.0525) 0.0525 PV = $579.6056 O Bond Value or Price = $359.3833+$579.6056 = $938.99