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.
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