Question

Consider a bond (with par value = $1,000) paying a coupon rate of 7% per year semiannually when the market interest rate is only 6% per half-year. The bond has 3 years until maturity.

  

a.	Find the bond's price today and 6 months from now after the next coupon is paid. (Round your answers to 2 decimal places. Omit the "$" sign in your response.)

  

Current price ____________	$
Price after six months __________	$

  

b.	What is the total (6-month) rate of return on the bond? (Omit the "%" sign in your response.)

  

Rate of return _____________

%

Answer 1

Answer a.

Current Price:

Par Value = $1,000

Annual Coupon Rate = 7%
Semiannual Coupon Rate = 3.50%
Semiannual Coupon = 3.50%*$1,000 = $35

Semiannual Interest Rate = 6%

Time to Maturity = 3 years
Semiannual Period to Maturity = 6

Price of Bond = $35 * PVIFA(6%, 6) + $1,000 * PVIF(6%, 6)
Price of Bond = $35 * (1 - (1/1.06)^6) / 0.06 + $1,000 / 1.06^6
Price of Bond = $877.07

Price after six months:

Par Value = $1,000
Semiannual Coupon = $35
Semiannual Interest Rate = 6%
Semiannual Period to Maturity = 5

Price of Bond = $35 * PVIFA(6%, 5) + $1,000 * PVIF(6%, 5)
Price of Bond = $35 * (1 - (1/1.06)^5) / 0.06 + $1,000 / 1.06^5
Price of Bond = $894.69

Answer b.

Rate of Return = ($894.69 + $35 - $877.07) / $877.07
Rate of Return = 6.00%