Question

# b.Suppose a​ ten-year, \$1,000 bond with an 8.8% coupon rate and semiannual coupons is trading for...

b.Suppose a​ ten-year, \$1,000 bond with an 8.8% coupon rate and semiannual coupons is trading for \$1,035.87.

a. What is the​ bond's yield to maturity​ (expressed as an APR with semiannual​ compounding)?

b. If the​ bond's yield to maturity changes to 9.6% ​APR, what will be the​ bond's price?

C. Suppose that General Motors Acceptance Corporation issued a bond with 10 years until​ maturity, a face value of \$1,000​, and a coupon rate of 7.6% ​(annual payments). The yield to maturity on this bond when it was issued was 5.9%. What was the price of this bond when it was​ issued? When it was issued, the price of the bond was \$____.

D. Suppose you purchase a 30​-year, ​zero-coupon bond with a yield to maturity of 5.5%. You hold the bond for five years before selling it.

a. If the​ bond's yield to maturity is 5.5% when you sell​ it, what is the annualized rate of return of your​ investment?

b. If the​ bond's yield to maturity is 6.5% when you sell​ it, what is the annualized rate of return of your​ investment?

c. If the​ bond's yield to maturity is 4.5% when you sell​ it, what is the annualized rate of return of your​ investment?

d. Even if a bond has no chance of​ default, is your investment risk free if you plan to sell it before it​ matures? Explain.

1.
a)
FV = 1000
PV = 1035.87
Nper = 10 * 2 = 20
PMT = 1000 * 8.8% / 2 = 44

Yield to maturity can be calculated by using the following excel formula:
=RATE(nper,pmt,pv,fv)*2
=RATE(20,44,-1035.87,1000)*2
= 8.27%

Yield to maturity = 8.27%

b)
Rate = 9.6% / 2 = 4.8%
Nper = 20
PMT = 1000 * 8.8% / 2 = 44
FV = 1000

Price of the bond can be calculated by using the following excel formula:
=PV(rate,nper,pmt,fv)
=PV(4.8%,20,-44,-1000)
= \$949.29

Price of the bond = \$949.29

2.
FV = \$1000
Nper = 10
PMT = 1000 * 7.6% = 76
Rate = 5.9%

Price of the bond can be calculated by using the following excel formula:
=PV(rate,nper,pmt,fv)
=PV(5.9%,10,-76,-1000)
= \$1,125.72

Price of the bond = \$1,125.72

Note: Post the rest of the questions separately