Question

Three years ago you purchased a $1,000 par 12-year bond with a 3.5% semi-annual coupon at a price of $875. If the current price is $965, what was the yield to maturity of the bond when it was purchased? A. 4.89% B. 3.97% C. 3.87% D. 5.26%

You purchased a $1,000 bond with a 4.6% semi-annual coupon and 15 years to maturity four years ago at a price of $855. If the yield has remained constant, what should be the price of the bond today? A. $971.56 B. $881.95 C. $547.34 D. $905.68

A 15-year, $1,000 par bond with a 6.5% semi-annual coupon currently trades at a price of $1,215. If the yield to maturity of the bond remains constant, what will be its price in six years? A. $1,145.73 B. $1,103.49 C. $846.71 D. $1,080.16 E. $1,268.00

Answer 1

1. The yield to maturity needs to be calculated using RATE function in EXCEL

=RATE(nper,pmt,pv,fv,type)

The bond is semi-annual coupon bond

nper=remaining periods=2*9=18 (12*24 periods in which already 3 years passed(3*2=6))

pmt=semi-annual coupon payment=(3.5%*1000)/2=35/2=17.5

pv=965

fv=1000

=RATE(18,17.5,-965,1000,0)=1.983%

RATE=semi-annual yield to maturity=1.983%

Annual yield to maturity=2*1.983%=3.97% (option B is correct)

2. First we have to find the yield to maturity using the same process mention as above

nper=15*2=30

pmt=(4.6%*1000)/2=46/2=23

pv=855

fv=1000

=RATE(30,23,-855,1000,0)=3.04%

Now, the Price of the bond has to be calculated using PV function in EXCEL

=PV(rate,nper,pmt,fv,type)

nper=remaining periods=11*2=22 (30-8)

rate=semi-annual yield to maturity=3.04%

pmt=23

fv=1000

=PV(3.04%,22,23,1000,0)

PV=$881.95 (Option B is correct)

3.We have to find this question same as 2nd question

First we have to find the yield to maturity using the same process mention as above

nper=15*2=30

pmt=(6.5%*1000)/2=65/2=32.5

pv=1215

fv=1000

=RATE(30,32.5,-1215,1000,0)=2.26%

Now, the Price of the bond has to be calculated using PV function in EXCEL

=PV(rate,nper,pmt,fv,type)

nper=remaining periods=9*2=18 (30-12)

rate=semi-annual yield to maturity=2.26%

pmt=32.5

fv=1000

=PV(2.26%,18,32.5,1000,0)

PV=$1145.73 (Option A is correct)