Question

You bought a 10-year, 5% coupon bond for $1000, and sold it 1 year later for $1,100. What is the rate of return on your investment if the bond pays interest annually? Semi-annually?

Answer 1

Answer a.

Purchase Price = $1,000
Selling Price = $1,100
Annual Coupon = 5%*$1,000 = $50

Rate of Return = (Selling Price + Annual Coupon - Purchase Price) / Purchase Price
Rate of Return = ($1,100 + $50 - $1,000) / $1,000
Rate of Return = 0.15
Rate of Return = 15%

Answer b.

Purchase Price = $1,000
Selling Price = $1,100
Annual Coupon = 5%
Semiannual Coupon = 2.5%*$1,000 = $25

Semiannual Rate of Return = [(Selling Price + 2 * Semiannual Coupon - Purchase Price) / Purchase Price + 1]^(1/2) - 1
Semiannual Rate of Return = [($1,100 + 2 * $25 - $1,000) / $1,000 + 1]^(1/2) - 1
Semiannual Rate of Return = (0.15 + 1)^(1/2) - 1
Semiannual Rate of Return = 1.15^(1/2) - 1
Semiannual Rate of Return = 1.0724 - 1
Semiannual Rate of Return = 7.24%

Annual Rate of Return = 2 * 7.24%
Annual Rate of Return = 14.48%