Final answer:
Bond K has a higher current yield than Bond J, as calculated using their coupon rates, yield to maturity (YTM), and current market prices.
Step-by-step explanation:
Bond J has a coupon rate of 4 percent and Bond K has a coupon rate of 10 percent. Both bonds have 17 years to maturity, make semiannual payments, and have a yield to maturity (YTM) of 7 percent. To determine which bond has a higher current yield, we need to calculate the current yield of each bond. The current yield is the annual interest payment divided by the bond's current market price.
Let's start by calculating the current yield of Bond J. Since it has a coupon rate of 4 percent and makes semiannual payments, the annual interest payment is 4% of the bond's face value. The bond's face value is $1,000, so the annual interest payment is $1,000 x 4% = $40. The current market price of Bond J will depend on its yield to maturity of 7 percent. We can use the formula for present value of a bond to calculate the current market price:
Current Market Price = (Coupon Payment/Discount Rate) x (1 - (1/(1+Discount Rate)^n)) + (Face Value/(1+Discount Rate)^n)
Plugging in the values, we get:
Current Market Price = ($40/7%) x (1 - (1/(1+7%)^(17x2))) + ($1,000/(1+7%)^(17x2))
Simplifying the calculation, we find that the current market price of Bond J is $949.98.
Now, let's calculate the current yield of Bond J:
Current Yield = Annual Interest Payment / Current Market Price = $40 / $949.98
Using a calculator, the current yield of Bond J is approximately 4.21%.
Next, let's calculate the current yield of Bond K. With a coupon rate of 10 percent and semiannual payments, the annual interest payment of Bond K is $1,000 x 10% = $100. The current market price of Bond K, again using the present value formula, is:
Current Market Price = ($100/7%) x (1 - (1/(1+7%)^(17x2))) + ($1,000/(1+7%)^(17x2))
Simplifying the calculation, we find that the current market price of Bond K is $1,266.74.
Lastly, we can calculate the current yield of Bond K:
Current Yield = Annual Interest Payment / Current Market Price = $100 / $1,266.74
Using a calculator, the current yield of Bond K is approximately 7.89%.
Comparing the current yields, we can conclude that Bond K has a higher current yield than Bond J.