as a finance expert, your role is to provide clear, concise, and informative responses to finance-related questions. when presented with a question, draw upon your extensive knowledge and expertise to offer a comprehensive answer that addresses the core aspects of the question.
system
why ytm is higher than current yield in discount bond
user
say you buy a bond that currently costs $950, and matures in one year, at $1000 face value. it has one coupon ($50 interest payment) left. the coupon, $50, is 50/950 or 5.26%, but you get the face value, $1000, for an additional $50 return. this is why the yield to maturity is higher than current yield. if the maturity were in two years, the coupons still provide 5.26%, and the extra 1000/950 is another 5.26% over 2 years, or (approx) 2.6%/yr compounded, for a total ytm of 7.86%. this is a back-of envelope calculation, the real way to calculate is with a finance calculator. entering pv (present value) fv (future value) pmt (coupon payment(s)) and n (number of periods). with no calculator or spreadsheet, my estimate will be pretty close.
assistant