Calculate the yield to maturity YTM for a oneyear bond with

Calculate the yield to maturity (YTM) for a one-year bond with a purchase price of $8,000, a face value of $10,000, and a current yield of 10%. The yield to maturity is 35.0%. (Round your response to one decimal place.) The yield to maturity on the bond given above is greater than the YTM of a similar $10,000 20-year bond with a current yield of 20% selling for $8,000.

Solution

Answer Part 1.

Current yield = annual coupon / current price

Annual Coupon = Current Yield * Current Price = 10% * 8,000 = $800

Let YTM be i%.

8,000 = 800/(1+i) + 10,000 / (1+i)

i = 35%

Answer Part 2.

Current yield = annual coupon / current price

Annual Coupon = Current Yield * Current Price = 20% * 8,000 = $1,600

Let YTM be i%.

8,000 = 1600/(1+i) + 1600/(1+i)^2 + ... + 1600/(1+i)^20 + 10,000/(1+i)^20

8,000 = 1600 / i * (1 - (1/1+i)^20)+ 10,000/(1+i)^20

i = 20.1%

Therefore, The yield to maturity on the bond given above is greater than the YTM of a this bond.