Assume that you have a bond with a 22-year life, a five percent coupon rate, semi-annual coupon payments and the bond is priced at 103.

a) What is the YTM
b) if the bond is callable after 3 yrs, What is the YTC?
c) What is the current yield?

To calculate the answers to these questions, we need to understand some key concepts related to bonds.

1. Yield to Maturity (YTM): This is the total return the investor can expect to receive by holding the bond until maturity. It takes into account the coupon payments, the bond's purchase price, and the time to maturity. To calculate YTM, we need to use the bond's cash flows and the market price.

2. Yield to Call (YTC): This is the yield an investor will earn if a bond is called (repurchased) before its maturity date. It is similar to YTM, but it considers the possibility of the bond being called before it matures.

3. Current Yield: This represents the bond's annual interest payment (coupon) divided by its current market price.

Now let's calculate the answers to the given questions:

a) YTM:
To calculate YTM, you would need to use the bond's cash flows (coupon payments) and its market price (103). The bond has a 5% coupon rate, which means it pays 2.5% semi-annually. Since the bond has a 22-year life, there will be 44 total coupon payments (22 years * 2 payments per year). However, the bond is priced at 103% of its face value, so the future cash flows need to be adjusted accordingly.

To calculate the YTM, you would set up an equation to find the discount rate that equates the present value of the bond's cash flows to its market price. You would then solve this equation using a financial calculator or software, or by using an iterative method in a spreadsheet.

b) YTC:
If the bond is callable after 3 years, you would use a similar approach as in calculating YTM. However, the difference here is that you need to consider different cash flows since the bond could be repurchased at a different time. You would need to calculate the cash flows up to the call date and use the adjusted market price for that period. After the call date, you will only consider the remaining cash flows till maturity. Then, follow the same process as in YTM to calculate YTC.

c) Current Yield:
To calculate the current yield, you need to divide the bond's annual interest payment (coupon) by its market price. In this case, the bond has a 5% coupon rate, which is equivalent to a 2.5% semi-annual coupon payment. Divide this by the bond's market price, which is 103, to get the current yield.

Remember that these calculations involve complex financial formulas and require precise inputs. It's recommended to use financial calculators, spreadsheets, or specialized software to perform these calculations accurately.