how to explain current yield
The current yield is a good approximation of the bond's yield, if the bond is selling at or near its face value or if it has a long maturity. That is, we noted earlier that if a bond is selling at par, its coupon rate is equal to the discount rate. In this case, the current yield is equal to the bond's yield to maturity. Thus, the closer the bond's price is to its face value, the closer the current yield is to the bond's yield to maturity. As for maturity, note that a coupon bond with no maturity or repayment of principal, known as a perpetuity or consul, pays a fixed amount of coupons forever. The value of such a bond is: