Question

A 4% semi-annual pay bond with a maturity of 10 years was sold to yield 6%. One year passes and interest rates remained unchanged at 6%. What will have happened to the bond's price during this period?

A. It will have increased

B. It will have decreased

C. It will have remained constant

Answer 1

Sol:

Coupon rate = 4% (semiannual) = 4%/2 = 2%

Period (nper) = 10 years (semiannual) = 10 x 2 = 20

Yield (Discount rate (r)) = 6% (semiannual) = 6%/2 = 3%

Face value = $1000 (Assumed)

PMT = 1000 x 2% = 20

Future value = $1000

Present value of bond will be as follows,

Price of Bond = PV(rate,nper,pmt,fv) (in excel)

Price of Bond = PV(3%,20,20,1000)

Price of Bond = $851.23

Now price of bond after 1 year will be as follows,

Period (nper) = 9 years (semiannual) = 9 x 2 = 18

All the other factors will remain same.

Price of Bond = PV(3%,18,20,1000)

Price of Bond = $862.46

We can make out that bond price has increased from $851.23 to $862.46 after one year.

Therefore answer is A. It will have increased