╨д╨╛╤А╨╝╤Г╨╗╨░ ╤Ж╨╡╨╜╨╛╨╛╨▒╤А╨░╨╖╨╛╨▓╨░╨╜╨╕╤П ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╣

╨д╨╛╤А╨╝╤Г╨╗╨░ ╨┤╨╗╤П ╤А╨░╤Б╤З╨╡╤В╨░ ╤Ж╨╡╨╜╤Л ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╕

╨д╨╛╤А╨╝╤Г╨╗╨░ ╨╛╤Ж╨╡╨╜╨║╨╕ ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╕╨Ю╤Ж╨╡╨╜╨║╨░ ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╕╨д╨╛╤А╨╝╤Г╨╗╨░ ╨╛╤Ж╨╡╨╜╨║╨╕ ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╕ ╤А╨░╤Б╤Б╤З╨╕╤В╤Л╨▓╨░╨╡╤В ╤В╨╡╨║╤Г╤Й╤Г╤О ╤Б╤В╨╛╨╕╨╝╨╛╤Б╤В╤М ╨▓╨╡╤А╨╛╤П╤В╨╜╤Л╤Е ╨▒╤Г╨┤╤Г╤Й╨╕╤Е ╨┤╨╡╨╜╨╡╨╢╨╜╤Л╤Е ╨┐╨╛╤В╨╛╨║╨╛╨▓, ╨║╨╛╤В╨╛╤А╤Л╨╡ ╨▓╨║╨╗╤О╤З╨░╤О╤В ╨║╤Г╨┐╨╛╨╜╨╜╤Л╨╡ ╨▓╤Л╨┐╨╗╨░╤В╤Л ╨╕ ╨╜╨╛╨╝╨╕╨╜╨░╨╗╤М╨╜╤Г╤О ╤Б╤В╨╛╨╕╨╝╨╛╤Б╤В╤М, ╨║╨╛╤В╨╛╤А╨░╤П ╨┐╤А╨╡╨┤╤Б╤В╨░╨▓╨╗╤П╨╡╤В ╤Б╨╛╨▒╨╛╨╣ ╤Б╤Г╨╝╨╝╤Г ╨┐╨╛╨│╨░╤И╨╡╨╜╨╕╤П ╨┐╤А╨╕ ╨┐╨╛╨│╨░╤И╨╡╨╜╨╕╨╕. ╨Ф╨╛╤Е╨╛╨┤╨╜╨╛╤Б╤В╤М ╨║ ╨┐╨╛╨│╨░╤И╨╡╨╜╨╕╤О (YTM) ╨╛╤В╨╜╨╛╤Б╨╕╤В╤Б╤П ╨║ ╨┐╤А╨╛╤Ж╨╡╨╜╤В╨╜╨╛╨╣ ╤Б╤В╨░╨▓╨║╨╡, ╨╕╤Б╨┐╨╛╨╗╤М╨╖╤Г╨╡╨╝╨╛╨╣ ╨┤╨╗╤П ╨┤╨╕╤Б╨║╨╛╨╜╤В╨╕╤А╨╛╨▓╨░╨╜╨╕╤П ╨▒╤Г╨┤╤Г╤Й╨╕╤Е ╨┤╨╡╨╜╨╡╨╢╨╜╤Л╤Е ╨┐╨╛╤В╨╛╨║╨╛╨▓. ╨Я╨╛╨┤╤А╨╛╨▒╨╜╨╡╨╡ тАФ ╤Н╤В╨╛ ╤А╨░╤Б╤З╨╡╤В ╨┐╤А╨╕╨▓╨╡╨┤╨╡╨╜╨╜╨╛╨╣ ╤Б╤В╨╛╨╕╨╝╨╛╤Б╤В╨╕ ╨▓╨╡╤А╨╛╤П╤В╨╜╤Л╤Е ╨▒╤Г╨┤╤Г╤Й╨╕╤Е ╨┤╨╡╨╜╨╡╨╢╨╜╤Л╤Е ╨┐╨╛╤В╨╛╨║╨╛╨▓, ╨║╨╛╤В╨╛╤А╤Л╨╣ ╨▓╨║╨╗╤О╤З╨░╨╡╤В ╨║╤Г╨┐╨╛╨╜╨╜╤Л╨╡ ╨▓╤Л╨┐╨╗╨░╤В╤Л ╨╕ ╨╜╨╛╨╝╨╕╨╜╨░╨╗╤М╨╜╤Г╤О ╤Б╤В╨╛╨╕╨╝╨╛╤Б╤В╤М, ╨║╨╛╤В╨╛╤А╨░╤П ╨┐╤А╨╡╨┤╤Б╤В╨░╨▓╨╗╤П╨╡╤В ╤Б╨╛╨▒╨╛╨╣ ╨┐╨╛╨│╨░╤И╨╡╨╜╨╕╨╡. ╤Б╤Г╨╝╨╝╨░ ╨┐╨╛ ╨╕╤Б╤В╨╡╤З╨╡╨╜╨╕╨╕ ╤Б╤А╨╛╨║╨░. ╨Я╤А╨╛╤Ж╨╡╨╜╤В╨╜╨░╤П ╤Б╤В╨░╨▓╨║╨░, ╨╕╤Б╨┐╨╛╨╗╤М╨╖╤Г╨╡╨╝╨░╤П ╨┤╨╗╤П ╨┤╨╕╤Б╨║╨╛╨╜╤В╨╕╤А╨╛╨▓╨░╨╜╨╕╤П ╨▒╤Г╨┤╤Г╤Й╨╕╤Е ╨┤╨╡╨╜╨╡╨╢╨╜╤Л╤Е ╨┐╨╛╤В╨╛╨║╨╛╨▓, ╨╕╨╖╨▓╨╡╤Б╤В╨╜╨░ ╨║╨░╨║ ╨┤╨╛╤Е╨╛╨┤╨╜╨╛╤Б╤В╤М ╨║ ╨┐╨╛╨│╨░╤И╨╡╨╜╨╕╤О (YTM).

╨ж╨╡╨╜╨░ ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╕ = тИСi=1n C/(1+r)n + F/(1+r)n

╨╕╨╗╨╕

╨ж╨╡╨╜╨░ ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╕ = C* (1-(1+r)-n/r ) + F/(1+r)n

╨│╨┤╨╡ C = ╨┐╨╡╤А╨╕╨╛╨┤╨╕╤З╨╡╤Б╨║╨░╤П ╨▓╤Л╨┐╨╗╨░╤В╨░ ╨║╤Г╨┐╨╛╨╜╨░,

• F = ╨╜╨╛╨╝╨╕╨╜╨░╨╗╤М╨╜╨░╤П / ╨╜╨╛╨╝╨╕╨╜╨░╨╗╤М╨╜╨░╤П ╤Б╤В╨╛╨╕╨╝╨╛╤Б╤В╤М ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╕,
• r = ╨┤╨╛╤Е╨╛╨┤╨╜╨╛╤Б╤В╤М ╨║ ╨┐╨╛╨│╨░╤И╨╡╨╜╨╕╤О (YTM) ╨╕
• n = ╨║╨╛╨╗╨╕╤З╨╡╤Б╤В╨▓╨╛ ╨┐╨╡╤А╨╕╨╛╨┤╨╛╨▓ ╨┤╨╛ ╨┐╨╛╨│╨░╤И╨╡╨╜╨╕╤П

╨б ╨┤╤А╤Г╨│╨╛╨╣ ╤Б╤В╨╛╤А╨╛╨╜╤Л, ╤Д╨╛╤А╨╝╤Г╨╗╨░ ╨╛╤Ж╨╡╨╜╨║╨╕ ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╣ ╨┤╨╗╤П ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╣ ╤Б ╨▒╨╛╨╗╤М╤И╨╕╨╝ ╨┤╨╕╤Б╨║╨╛╨╜╤В╨╛╨╝ ╨╕╨╗╨╕ ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╣ ╤Б ╨╜╤Г╨╗╨╡╨▓╤Л╨╝ ╨║╤Г╨┐╨╛╨╜╨╛╨╝╨Ю╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╕ ╤Б ╨╜╤Г╨╗╨╡╨▓╤Л╨╝ ╨║╤Г╨┐╨╛╨╜╨╛╨╝╨Т ╨╛╤В╨╗╨╕╤З╨╕╨╡ ╨╛╤В ╨╛╨▒╤Л╤З╨╜╤Л╤Е ╨║╤Г╨┐╨╛╨╜╨╜╤Л╤Е ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╣, ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╤П ╤Б ╨╜╤Г╨╗╨╡╨▓╤Л╨╝ ╨║╤Г╨┐╨╛╨╜╨╛╨╝ (╤В╨░╨║╨╢╨╡ ╨╕╨╖╨▓╨╡╤Б╤В╨╜╨░╤П ╨║╨░╨║ ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╤П ╤Б ╤З╨╕╤Б╤В╤Л╨╝ ╨┤╨╕╤Б╨║╨╛╨╜╤В╨╛╨╝ ╨╕╨╗╨╕ ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╤П ╤Б ╨╜╨░╨║╨╛╨┐╨╗╨╡╨╜╨╕╨╡╨╝) ╨┐╤А╨╡╨┤╤Б╤В╨░╨▓╨╗╤П╨╡╤В ╤Б╨╛╨▒╨╛╨╣ ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╤О, ╨║╨╛╤В╨╛╤А╨░╤П ╨▓╤Л╨┐╤Г╤Б╨║╨░╨╡╤В╤Б╤П ╤Б╨╛ ╤Б╨║╨╕╨┤╨║╨╛╨╣ ╨║ ╨╜╨╛╨╝╨╕╨╜╨░╨╗╤М╨╜╨╛╨╣ ╤Б╤В╨╛╨╕╨╝╨╛╤Б╤В╨╕ ╨╕ ╨╜╨╡ ╨┤╨░╨╡╤В ╨┐╨╡╤А╨╕╨╛╨┤╨╕╤З╨╡╤Б╨║╨╕╤Е ╨┐╤А╨╛╤Ж╨╡╨╜╤В╨╛╨▓. ╨Ф╤А╤Г╨│╨╕╨╝╨╕ ╤Б╨╗╨╛╨▓╨░╨╝╨╕, ╨╡╨╢╨╡╨│╨╛╨┤╨╜╤Л╨╣ ╨┐╨╛╨┤╤А╨░╨╖╤Г╨╝╨╡╨▓╨░╨╡╨╝╤Л╨╣ ╨┐╤А╨╛╤Ж╨╡╨╜╤В╨╜╤Л╨╣ ╨┐╨╗╨░╤В╨╡╨╢ ╨▓╨║╨╗╤О╤З╨░╨╡╤В╤Б╤П ╨▓ ╨╜╨╛╨╝╨╕╨╜╨░╨╗╤М╨╜╤Г╤О ╤Б╤В╨╛╨╕╨╝╨╛╤Б╤В╤М ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╕, ╨║╨╛╤В╨╛╤А╨░╤П ╨▓╤Л╨┐╨╗╨░╤З╨╕╨▓╨░╨╡╤В╤Б╤П ╨┐╤А╨╕ ╨┐╨╛╨│╨░╤И╨╡╨╜╨╕╨╕. ╨Т ╤А╨╡╨╖╤Г╨╗╤М╤В╨░╤В╨╡ ╤Г ╤Н╤В╨╛╨╣ ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╕ ╨╡╤Б╤В╤М ╤В╨╛╨╗╤М╨║╨╛ ╨╛╨┤╨╕╨╜ ╨┤╨╛╤Е╨╛╨┤: ╨▓╤Л╨┐╨╗╨░╤В╨░ ╨╜╨╛╨╝╨╕╨╜╨░╨╗╤М╨╜╨╛╨╣ ╤Б╤В╨╛╨╕╨╝╨╛╤Б╤В╨╕ ╨┐╤А╨╕ ╨┐╨╛╨│╨░╤И╨╡╨╜╨╕╨╕. ╨С╨╛╨╗╨╡╨╡ ╨┐╨╛╨┤╤А╨╛╨▒╨╜╨░╤П ╨╕╨╜╤Д╨╛╤А╨╝╨░╤Ж╨╕╤П ╨╝╨╛╨╢╨╡╤В ╨▒╤Л╤В╤М ╤А╨░╤Б╤Б╤З╨╕╤В╨░╨╜╨░ ╨┐╤А╨╛╤Б╤В╨╛ ╨┐╤Г╤В╨╡╨╝ ╨┤╨╕╤Б╨║╨╛╨╜╤В╨╕╤А╨╛╨▓╨░╨╜╨╕╤П ╨╜╨╛╨╝╨╕╨╜╨░╨╗╤М╨╜╨╛╨╣ ╤Б╤В╨╛╨╕╨╝╨╛╤Б╤В╨╕ ╨┤╨╛ ╤В╨╡╨║╤Г╤Й╨╡╨╣ ╤Б╤В╨╛╨╕╨╝╨╛╤Б╤В╨╕, ╨║╨╛╤В╨╛╤А╨░╤П ╨╝╨░╤В╨╡╨╝╨░╤В╨╕╤З╨╡╤Б╨║╨╕ ╨┐╤А╨╡╨┤╤Б╤В╨░╨▓╨╗╨╡╨╜╨░ тАЛтАЛ╨║╨░╨║

╨ж╨╡╨╜╨░ ╨▒╨╡╤Б╨║╤Г╨┐╨╛╨╜╨╜╨╛╨╣ ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╕ = (╨║╨░╨║ ╤Б╨╗╨╡╨┤╤Г╨╡╤В ╨╕╨╖ ╨╜╨░╨╖╨▓╨░╨╜╨╕╤П, ╨║╤Г╨┐╨╛╨╜╨╜╤Л╨╡ ╨▓╤Л╨┐╨╗╨░╤В╤Л ╨╛╤В╤Б╤Г╤В╤Б╤В╨▓╤Г╤О╤В)

╨Ю╨│╨╗╨░╨▓╨╗╨╡╨╜╨╕╨╡

• ╨д╨╛╤А╨╝╤Г╨╗╨░ ╨┤╨╗╤П ╤А╨░╤Б╤З╨╡╤В╨░ ╤Ж╨╡╨╜╤Л ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╕
  • ╨а╨░╤Б╤З╨╡╤В ╤Б╤В╨╛╨╕╨╝╨╛╤Б╤В╨╕ ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╕ (╤И╨░╨│ ╨╖╨░ ╤И╨░╨│╨╛╨╝)
  • ╨Я╤А╨░╨║╤В╨╕╤З╨╡╤Б╨║╨╕╨╡ ╨┐╤А╨╕╨╝╨╡╤А╤Л (╤Б ╤И╨░╨▒╨╗╨╛╨╜╨╛╨╝ Excel)
    • ╨Я╤А╨╕╨╝╨╡╤А тДЦ1
    • ╨Я╤А╨╕╨╝╨╡╤А #2
    • ╨Я╤А╨╕╨╝╨╡╤А тДЦ3
  • ╨Ш╤Б╨┐╨╛╨╗╤М╨╖╨╛╨▓╨░╨╜╨╕╨╡ ╨╕ ╨░╨║╤В╤Г╨░╨╗╤М╨╜╨╛╤Б╤В╤М
  • ╨Т╨╕╨┤╨╡╨╛ ╨╛ ╤Д╨╛╤А╨╝╤Г╨╗╨╡ ╤Ж╨╡╨╜╨╛╨╛╨▒╤А╨░╨╖╨╛╨▓╨░╨╜╨╕╤П ╨╜╨░ ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╕
  • ╨а╨╡╨║╨╛╨╝╨╡╨╜╨┤╤Г╨╡╨╝╤Л╨╡ ╤Б╤В╨░╤В╤М╨╕

╨а╨░╤Б╤З╨╡╤В ╤Б╤В╨╛╨╕╨╝╨╛╤Б╤В╨╕ ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╕ (╤И╨░╨│ ╨╖╨░ ╤И╨░╨│╨╛╨╝)

╨д╨╛╤А╨╝╤Г╨╗╨░ ╨┤╨╗╤П ╤А╨░╤Б╤З╨╡╤В╨░ ╤Ж╨╡╨╜╤Л ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╕ ╤Б ╨╕╤Б╨┐╨╛╨╗╤М╨╖╨╛╨▓╨░╨╜╨╕╨╡╨╝ ╤Б╨╗╨╡╨┤╤Г╤О╤Й╨╕╤Е ╤И╨░╨│╨╛╨▓:

1. ╨Т╨╛-╨┐╨╡╤А╨▓╤Л╤Е, ╨╜╨╛╨╝╨╕╨╜╨░╨╗╤М╨╜╨░╤П ╤Б╤В╨╛╨╕╨╝╨╛╤Б╤В╤М ╨╕╨╗╨╕ ╨╜╨╛╨╝╨╕╨╜╨░╨╗╤М╨╜╨░╤П ╤Б╤В╨╛╨╕╨╝╨╛╤Б╤В╤М ╨▓╤Л╨┐╤Г╤Б╨║╨░ ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╣ ╨╛╨┐╤А╨╡╨┤╨╡╨╗╤П╨╡╤В╤Б╤П ╨▓ ╤Б╨╛╨╛╤В╨▓╨╡╤В╤Б╤В╨▓╨╕╨╕ ╤Б ╨┐╨╛╤В╤А╨╡╨▒╨╜╨╛╤Б╤В╤М╤О ╨║╨╛╨╝╨┐╨░╨╜╨╕╨╕ ╨▓ ╤Д╨╕╨╜╨░╨╜╤Б╨╕╤А╨╛╨▓╨░╨╜╨╕╨╕. ╨Э╨╛╨╝╨╕╨╜╨░╨╗╤М╨╜╨░╤П ╤Б╤В╨╛╨╕╨╝╨╛╤Б╤В╤М ╨╛╨▒╨╛╨╖╨╜╨░╤З╨╡╨╜╨░ ╨▒╤Г╨║╨▓╨╛╨╣ F.

2. ╨в╨╡╨┐╨╡╤А╤М ╨╛╨┐╤А╨╡╨┤╨╡╨╗╤П╨╡╤В╤Б╤П ╨║╤Г╨┐╨╛╨╜╨╜╨░╤П ╤Б╤В╨░╨▓╨║╨░, ╨░╨╜╨░╨╗╨╛╨│╨╕╤З╨╜╨░╤П ╨┐╤А╨╛╤Ж╨╡╨╜╤В╨╜╨╛╨╣ ╤Б╤В╨░╨▓╨║╨╡ ╨┐╨╛ ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╕, ╨╕ ╨┐╨╡╤А╨╕╨╛╨┤╨╕╤З╨╜╨╛╤Б╤В╤М ╨║╤Г╨┐╨╛╨╜╨╜╨╛╨╣ ╨▓╤Л╨┐╨╗╨░╤В╤Л. ╨Т╤Л╨┐╨╗╨░╤В╨░ ╨║╤Г╨┐╨╛╨╜╨░ ╨╖╨░ ╨┐╨╡╤А╨╕╨╛╨┤ ╤А╨░╤Б╤Б╤З╨╕╤В╤Л╨▓╨░╨╡╤В╤Б╤П ╨┐╤Г╤В╨╡╨╝ ╤Г╨╝╨╜╨╛╨╢╨╡╨╜╨╕╤П ╤Б╤В╨░╨▓╨║╨╕ ╨║╤Г╨┐╨╛╨╜╨░ ╨╜╨░ ╨╜╨╛╨╝╨╕╨╜╨░╨╗╤М╨╜╤Г╤О ╤Б╤В╨╛╨╕╨╝╨╛╤Б╤В╤М ╨╕ ╨┐╨╛╤Б╨╗╨╡╨┤╤Г╤О╤Й╨╡╨│╨╛ ╨┤╨╡╨╗╨╡╨╜╨╕╤П ╤А╨╡╨╖╤Г╨╗╤М╤В╨░╤В╨░ ╨╜╨░ ╤З╨░╤Б╤В╨╛╤В╤Г ╨▓╤Л╨┐╨╗╨░╤В╤Л ╨║╤Г╨┐╨╛╨╜╨░ ╨▓ ╤В╨╡╤З╨╡╨╜╨╕╨╡ ╨│╨╛╨┤╨░. ╨Т╤Л╨┐╨╗╨░╤В╨░ ╨║╤Г╨┐╨╛╨╜╨░ ╨╛╨▒╨╛╨╖╨╜╨░╤З╨╡╨╜╨░ ╨▒╤Г╨║╨▓╨╛╨╣ C.

   C = ╨║╤Г╨┐╨╛╨╜╨╜╨░╤П ╤Б╤В╨░╨▓╨║╨░ * F / ╨║╨╛╨╗╨╕╤З╨╡╤Б╤В╨▓╨╛ ╨║╤Г╨┐╨╛╨╜╨╜╤Л╤Е ╨▓╤Л╨┐╨╗╨░╤В ╨▓ ╨│╨╛╨┤╤Г

3. ╨Ю╨▒╤Й╨╡╨╡ ╨║╨╛╨╗╨╕╤З╨╡╤Б╤В╨▓╨╛ ╨┐╨╡╤А╨╕╨╛╨┤╨╛╨▓ ╨┤╨╛ ╨┐╨╛╨│╨░╤И╨╡╨╜╨╕╤П ╤А╨░╤Б╤Б╤З╨╕╤В╤Л╨▓╨░╨╡╤В╤Б╤П ╨┐╤Г╤В╨╡╨╝ ╤Г╨╝╨╜╨╛╨╢╨╡╨╜╨╕╤П ╨║╨╛╨╗╨╕╤З╨╡╤Б╤В╨▓╨░ ╨╗╨╡╤В ╨┤╨╛ ╨┐╨╛╨│╨░╤И╨╡╨╜╨╕╤П ╨╕ ╤З╨░╤Б╤В╨╛╤В╤Л ╨║╤Г╨┐╨╛╨╜╨╜╤Л╤Е ╨▓╤Л╨┐╨╗╨░╤В ╨▓ ╨│╨╛╨┤╤Г. ╨Ъ╨╛╨╗╨╕╤З╨╡╤Б╤В╨▓╨╛ ╨┐╨╡╤А╨╕╨╛╨┤╨╛╨▓ ╨┤╨╛ ╨┐╨╛╨│╨░╤И╨╡╨╜╨╕╤П ╨╛╨▒╨╛╨╖╨╜╨░╤З╨░╨╡╤В╤Б╤П n.

   n = ╨║╨╛╨╗╨╕╤З╨╡╤Б╤В╨▓╨╛ ╨╗╨╡╤В ╨┤╨╛ ╨┐╨╛╨│╨░╤И╨╡╨╜╨╕╤П * ╨║╨╛╨╗╨╕╤З╨╡╤Б╤В╨▓╨╛ ╨║╤Г╨┐╨╛╨╜╨╜╤Л╤Е ╨▓╤Л╨┐╨╗╨░╤В ╨▓ ╨│╨╛╨┤╤Г

4. YTM тАФ ╤Н╤В╨╛ ╨║╨╛╤Н╤Д╤Д╨╕╤Ж╨╕╨╡╨╜╤В ╨┤╨╕╤Б╨║╨╛╨╜╤В╨╕╤А╨╛╨▓╨░╨╜╨╕╤П, ╨║╨╛╤В╨╛╤А╤Л╨╣ ╨╛╨┐╤А╨╡╨┤╨╡╨╗╤П╨╡╤В╤Б╤П ╨╜╨░ ╨╛╤Б╨╜╨╛╨▓╨╡ ╤В╨╡╨║╤Г╤Й╨╡╨╣ ╤А╤Л╨╜╨╛╤З╨╜╨╛╨╣ ╨┤╨╛╤Е╨╛╨┤╨╜╨╛╤Б╤В╨╕ ╨╕╨╜╨▓╨╡╤Б╤В╨╕╤Ж╨╕╨╣ ╤Б ╨░╨╜╨░╨╗╨╛╨│╨╕╤З╨╜╤Л╨╝ ╨┐╤А╨╛╤Д╨╕╨╗╨╡╨╝ ╤А╨╕╤Б╨║╨░. YTM ╨╛╨▒╨╛╨╖╨╜╨░╤З╨░╨╡╤В╤Б╤П r.

5. ╨в╨╡╨┐╨╡╤А╤М ╨┐╤А╨╕╨▓╨╡╨┤╨╡╨╜╨╜╨░╤П ╤Б╤В╨╛╨╕╨╝╨╛╤Б╤В╤М ╨┐╨╡╤А╨▓╨╛╨│╨╛, ╨▓╤В╨╛╤А╨╛╨│╨╛, ╤В╤А╨╡╤В╤М╨╡╨│╨╛ ╨║╤Г╨┐╨╛╨╜╨╜╨╛╨│╨╛ ╨┐╨╗╨░╤В╨╡╨╢╨░ ╨╕ ╤В. ╨┤. ╨▓╨╝╨╡╤Б╤В╨╡ ╤Б ╨┐╤А╨╕╨▓╨╡╨┤╨╡╨╜╨╜╨╛╨╣ ╤Б╤В╨╛╨╕╨╝╨╛╤Б╤В╤М╤О ╨╜╨╛╨╝╨╕╨╜╨░╨╗╤М╨╜╨╛╨╣ ╤Б╤В╨╛╨╕╨╝╨╛╤Б╤В╨╕, ╨┐╨╛╨┤╨╗╨╡╨╢╨░╤Й╨╡╨╣ ╨┐╨╛╨│╨░╤И╨╡╨╜╨╕╤О ╤З╨╡╤А╨╡╨╖ n ╨┐╨╡╤А╨╕╨╛╨┤╨╛╨▓, ╨╛╨┐╤А╨╡╨┤╨╡╨╗╤П╨╡╤В╤Б╤П ╨║╨░╨║

   

   

   

   

   

6. ╨Э╨░╨║╨╛╨╜╨╡╤Ж, ╤Б╤Г╨╝╨╝╨╕╤А╤Г╤П ╤В╨╡╨║╤Г╤Й╤Г╤О ╤Б╤В╨╛╨╕╨╝╨╛╤Б╤В╤М ╨▓╤Б╨╡╤Е ╨║╤Г╨┐╨╛╨╜╨╜╤Л╤Е ╨▓╤Л╨┐╨╗╨░╤В ╨╕ ╨╜╨╛╨╝╨╕╨╜╨░╨╗╤М╨╜╤Г╤О ╤Б╤В╨╛╨╕╨╝╨╛╤Б╤В╤М, ╨╝╤Л ╨┐╨╛╨╗╤Г╤З╨░╨╡╨╝ ╤Ж╨╡╨╜╤Г ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╕, ╨║╨░╨║ ╨┐╨╛╨║╨░╨╖╨░╨╜╨╛ ╨╜╨╕╨╢╨╡:

   

╨Я╤А╨░╨║╤В╨╕╤З╨╡╤Б╨║╨╕╨╡ ╨┐╤А╨╕╨╝╨╡╤А╤Л (╤Б ╤И╨░╨▒╨╗╨╛╨╜╨╛╨╝ Excel)

.free_excel_div{╤Д╨╛╨╜:#d9d9d9;╤А╨░╨╖╨╝╨╡╤А ╤И╤А╨╕╤Д╤В╨░:16px;╤А╨░╨┤╨╕╤Г╤Б ╨│╤А╨░╨╜╨╕╤Ж╤Л:7px;╨┐╨╛╨╖╨╕╤Ж╨╕╤П:╨╛╤В╨╜╨╛╤Б╨╕╤В╨╡╨╗╤М╨╜╨░╤П;margin:30px;padding:25px 25px 25px 45px}.free_excel_div:before{content:»»;╤Д╨╛╨╜:url(╤Ж╨╡╨╜╤В╤А ╤Ж╨╡╨╜╤В╤А ╨▒╨╡╨╖ ╨┐╨╛╨▓╤В╨╛╤А╨░ #207245;╤И╨╕╤А╨╕╨╜╨░:70px;╨▓╤Л╤Б╨╛╤В╨░:70px;╨┐╨╛╨╖╨╕╤Ж╨╕╤П:╨░╨▒╤Б╨╛╨╗╤О╤В╨╜╨░╤П;╨▓╨╡╤А╤Е:50%;margin-top:-35px;╤Б╨╗╨╡╨▓╨░:-35px;╨│╤А╨░╨╜╨╕╤Ж╨░:5px ╤Б╨┐╨╗╨╛╤И╨╜╨░╤П #fff;╨│╤А╨░╨╜╨╕╤Ж╨░-╤А╨░╨┤╨╕╤Г╤Б:50%} ╨Т╤Л ╨╝╨╛╨╢╨╡╤В╨╡ ╤Б╨║╨░╤З╨░╤В╤М ╤Н╤В╨╛╤В ╤И╨░╨▒╨╗╨╛╨╜ Excel ╤Б ╤Д╨╛╤А╨╝╤Г╨╗╨╛╨╣ ╤Ж╨╡╨╜╨╛╨╛╨▒╤А╨░╨╖╨╛╨▓╨░╨╜╨╕╤П ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╣ ╨╖╨┤╨╡╤Б╤М тАУ ╨д╨╛╤А╨╝╤Г╨╗╨░ ╤Ж╨╡╨╜╨╛╨╛╨▒╤А╨░╨╖╨╛╨▓╨░╨╜╨╕╤П ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╣ ╨и╨░╨▒╨╗╨╛╨╜ Excel

╨Я╤А╨╕╨╝╨╡╤А тДЦ1

╨Т╨╛╨╖╤М╨╝╨╡╨╝ ╨┐╤А╨╕╨╝╨╡╤А ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╕. ╨Я╤А╨╕╨╝╨╡╤А ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╕ ╨Ю╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╕ ╨╛╤В╨╜╨╛╤Б╤П╤В╤Б╤П ╨║ ╨┤╨╛╨╗╨│╨╛╨▓╤Л╨╝ ╨╕╨╜╤Б╤В╤А╤Г╨╝╨╡╨╜╤В╨░╨╝, ╨▓╤Л╨┐╤Г╤Й╨╡╨╜╨╜╤Л╨╝ ╨┐╤А╨░╨▓╨╕╤В╨╡╨╗╤М╤Б╤В╨▓╨░╨╝╨╕ ╨╕╨╗╨╕ ╨║╨╛╤А╨┐╨╛╤А╨░╤Ж╨╕╤П╨╝╨╕ ╨┤╨╗╤П ╨┐╤А╨╕╨╛╨▒╤А╨╡╤В╨╡╨╜╨╕╤П ╤Б╤А╨╡╨┤╤Б╤В╨▓ ╨╕╨╜╨▓╨╡╤Б╤В╨╛╤А╨╛╨▓ ╨╜╨░ ╨╛╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╜╤Л╨╣ ╨┐╨╡╤А╨╕╨╛╨┤. ╨Я╨╛╨┤╤А╨╛╨▒╨╜╨╡╨╡ ╤Б ╨╡╨╢╨╡╨│╨╛╨┤╨╜╤Л╨╝╨╕ ╨║╤Г╨┐╨╛╨╜╨╜╤Л╨╝╨╕ ╨▓╤Л╨┐╨╗╨░╤В╨░╨╝╨╕. ╨Я╤А╨╡╨┤╨┐╨╛╨╗╨╛╨╢╨╕╨╝, ╨║╨╛╨╝╨┐╨░╨╜╨╕╤П XYZ Ltd ╨▓╤Л╨┐╤Г╤Б╤В╨╕╨╗╨░ ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╤О ╨╜╨╛╨╝╨╕╨╜╨░╨╗╤М╨╜╨╛╨╣ ╤Б╤В╨╛╨╕╨╝╨╛╤Б╤В╤М╤О 100 000 ╨┤╨╛╨╗╨╗╨░╤А╨╛╨▓ ╨б╨и╨Р ╤Б ╨│╨╛╨┤╨╛╨▓╨╛╨╣ ╨║╤Г╨┐╨╛╨╜╨╜╨╛╨╣ ╤Б╤В╨░╨▓╨║╨╛╨╣ 7% ╨╕ ╤Б╤А╨╛╨║╨╛╨╝ ╨┐╨╛╨│╨░╤И╨╡╨╜╨╕╤П 15 ╨╗╨╡╤В. ╨Я╤А╨╡╨╛╨▒╨╗╨░╨┤╨░╤О╤Й╨░╤П ╤А╤Л╨╜╨╛╤З╨╜╨░╤П ╨┐╤А╨╛╤Ж╨╡╨╜╤В╨╜╨░╤П ╤Б╤В╨░╨▓╨║╨░ ╤Б╨╛╤Б╤В╨░╨▓╨╗╤П╨╡╤В 9%.

• ╨Ф╨░╨╜╨╛, F = 100 000 ╨┤╨╛╨╗╨╗╨░╤А╨╛╨▓.
• ╨б = 7% * 100 000 ╨┤╨╛╨╗╨╗╨░╤А╨╛╨▓ = 7 000 ╨┤╨╛╨╗╨╗╨░╤А╨╛╨▓.
• ╨┐ = 15
• ╨│ = 9%

╨ж╨╡╨╜╨░ ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╕ ╤А╨░╤Б╤Б╤З╨╕╤В╤Л╨▓╨░╨╡╤В╤Б╤П ╨┐╨╛ ╨┐╤А╨╕╨▓╨╡╨┤╨╡╨╜╨╜╨╛╨╣ ╨▓╤Л╤И╨╡ ╤Д╨╛╤А╨╝╤Г╨╗╨╡ ╨║╨░╨║,

• ╨ж╨╡╨╜╨░ ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╕ = 83 878,62 ╨┤╨╛╨╗╨╗. ╨б╨и╨Р

╨Я╨╛╤Б╨║╨╛╨╗╤М╨║╤Г ╨║╤Г╨┐╨╛╨╜╨╜╨░╤П ╤Б╤В╨░╨▓╨║╨░╨б╤В╨░╨▓╨║╨░ ╨║╤Г╨┐╨╛╨╜╨░╨б╤В╨░╨▓╨║╨░ ╨║╤Г╨┐╨╛╨╜╨░ тАФ ╤Н╤В╨╛ ROI (╨┐╤А╨╛╤Ж╨╡╨╜╤В╨╜╨░╤П ╤Б╤В╨░╨▓╨║╨░), ╨▓╤Л╨┐╨╗╨░╤З╨╕╨▓╨░╨╡╨╝╨░╤П ╤Н╨╝╨╕╤В╨╡╨╜╤В╨░╨╝╨╕ ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╕ ╨┐╨╛ ╨╜╨╛╨╝╨╕╨╜╨░╨╗╤М╨╜╨╛╨╣ ╤Б╤В╨╛╨╕╨╝╨╛╤Б╤В╨╕ ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╕. ╨Ю╨╜ ╨╛╨┐╤А╨╡╨┤╨╡╨╗╤П╨╡╤В ╤Б╤Г╨╝╨╝╤Г ╨┐╨╛╨│╨░╤И╨╡╨╜╨╕╤П, ╨┐╤А╨╛╨╕╨╖╨▓╨╛╨┤╨╕╨╝╤Г╤О ╨У╨Ш╨б (╨│╨░╤А╨░╨╜╤В╨╕╤А╨╛╨▓╨░╨╜╨╜╨░╤П ╨│╨░╤А╨░╨╜╤В╨╕╤П ╨┤╨╛╤Е╨╛╨┤╨░). ╨Ъ╤Г╨┐╨╛╨╜╨╜╨░╤П ╤Б╤В╨░╨▓╨║╨░ = ╨У╨╛╨┤╨╛╨▓╨╛╨╣ ╨┐╤А╨╛╤Ж╨╡╨╜╤В╨╜╤Л╨╣ ╨┐╨╗╨░╤В╨╡╨╢ / ╨Э╨╛╨╝╨╕╨╜╨░╨╗╤М╨╜╨░╤П ╤Б╤В╨╛╨╕╨╝╨╛╤Б╤В╤М ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╕ * 100%╨з╨╕╤В╨░╤В╤М ╨┤╨░╨╗╨╡╨╡ ╨╜╨╕╨╢╨╡, ╤З╨╡╨╝ YTM, ╤Ж╨╡╨╜╨░ ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╕ ╨╝╨╡╨╜╤М╤И╨╡ ╨╜╨╛╨╝╨╕╨╜╨░╨╗╤М╨╜╨╛╨╣ ╤Б╤В╨╛╨╕╨╝╨╛╤Б╤В╨╕, ╨╕ ╨┐╨╛╤Н╤В╨╛╨╝╤Г ╤Б╤З╨╕╤В╨░╨╡╤В╤Б╤П, ╤З╤В╨╛ ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╤П ╤В╨╛╤А╨│╤Г╨╡╤В╤Б╤П ╤Б ╨┤╨╕╤Б╨║╨╛╨╜╤В╨╛╨╝.

╨Я╤А╨╕╨╝╨╡╤А #2

╨Т╨╛╨╖╤М╨╝╨╡╨╝ ╨┐╤А╨╕╨╝╨╡╤А ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╕ ╤Б ╨┐╨╛╨╗╤Г╨│╨╛╨┤╨╛╨▓╤Л╨╝╨╕ ╨║╤Г╨┐╨╛╨╜╨╜╤Л╨╝╨╕ ╨▓╤Л╨┐╨╗╨░╤В╨░╨╝╨╕. ╨Я╤А╨╡╨┤╨┐╨╛╨╗╨╛╨╢╨╕╨╝, ╨║╨╛╨╝╨┐╨░╨╜╨╕╤П ABC Ltd ╨▓╤Л╨┐╤Г╤Б╤В╨╕╨╗╨░ ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╤О ╨╜╨╛╨╝╨╕╨╜╨░╨╗╤М╨╜╨╛╨╣ ╤Б╤В╨╛╨╕╨╝╨╛╤Б╤В╤М╤О 100 000 ╨┤╨╛╨╗╨╗╨░╤А╨╛╨▓ ╤Б╨╛ ╤Б╤В╨░╨▓╨║╨╛╨╣ ╨║╤Г╨┐╨╛╨╜╨░ 8%, ╨▓╤Л╨┐╨╗╨░╤З╨╕╨▓╨░╨╡╨╝╨╛╨╣ ╤А╨░╨╖ ╨▓ ╨┐╨╛╨╗╨│╨╛╨┤╨░, ╤Б╨╛ ╤Б╤А╨╛╨║╨╛╨╝ ╨┐╨╛╨│╨░╤И╨╡╨╜╨╕╤П 5 ╨╗╨╡╤В. ╨Я╤А╨╡╨╛╨▒╨╗╨░╨┤╨░╤О╤Й╨░╤П ╤А╤Л╨╜╨╛╤З╨╜╨░╤П ╨┐╤А╨╛╤Ж╨╡╨╜╤В╨╜╨░╤П ╤Б╤В╨░╨▓╨║╨░ ╤Б╨╛╤Б╤В╨░╨▓╨╗╤П╨╡╤В 7%.

╨б╨╗╨╡╨┤╨╛╨▓╨░╤В╨╡╨╗╤М╨╜╨╛, ╤Ж╨╡╨╜╨░ ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╕ ╤А╨░╤Б╤Б╤З╨╕╤В╤Л╨▓╨░╨╡╤В╤Б╤П ╨┐╨╛ ╨┐╤А╨╕╨▓╨╡╨┤╨╡╨╜╨╜╨╛╨╣ ╨▓╤Л╤И╨╡ ╤Д╨╛╤А╨╝╤Г╨╗╨╡ ╤Б╨╗╨╡╨┤╤Г╤О╤Й╨╕╨╝ ╨╛╨▒╤А╨░╨╖╨╛╨╝:

• ╨ж╨╡╨╜╨░ ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╕ = 104 158,30 ╨┤╨╛╨╗╨╗╨░╤А╨╛╨▓ ╨б╨и╨Р.

╨Я╨╛╤Б╨║╨╛╨╗╤М╨║╤Г ╨║╤Г╨┐╨╛╨╜╨╜╨░╤П ╤Б╤В╨░╨▓╨║╨░ ╨▓╤Л╤И╨╡, ╤З╨╡╨╝ YTM, ╤Ж╨╡╨╜╨░ ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╕ ╨▓╤Л╤И╨╡ ╨╜╨╛╨╝╨╕╨╜╨░╨╗╤М╨╜╨╛╨╣ ╤Б╤В╨╛╨╕╨╝╨╛╤Б╤В╨╕, ╨╕ ╨┐╨╛╤Н╤В╨╛╨╝╤Г ╨│╨╛╨▓╨╛╤А╤П╤В, ╤З╤В╨╛ ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╤П ╤В╨╛╤А╨│╤Г╨╡╤В╤Б╤П ╨┐╨╛ ╤Ж╨╡╨╜╨╡ ╨┐╤А╨╡╨╝╨╕╤П

╨Я╤А╨╕╨╝╨╡╤А тДЦ3

╨Т╨╛╨╖╤М╨╝╨╡╨╝ ╨▓ ╨║╨░╤З╨╡╤Б╤В╨▓╨╡ ╨┐╤А╨╕╨╝╨╡╤А╨░ ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╤О ╤Б ╨╜╤Г╨╗╨╡╨▓╤Л╨╝ ╨║╤Г╨┐╨╛╨╜╨╛╨╝. ╨Я╤А╨╡╨┤╨┐╨╛╨╗╨╛╨╢╨╕╨╝, ╨║╨╛╨╝╨┐╨░╨╜╨╕╤П QPR Ltd ╨▓╤Л╨┐╤Г╤Б╤В╨╕╨╗╨░ ╨▒╨╡╤Б╨║╤Г╨┐╨╛╨╜╨╜╤Л╨╡ ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╕ ╨╜╨╛╨╝╨╕╨╜╨░╨╗╤М╨╜╨╛╨╣ ╤Б╤В╨╛╨╕╨╝╨╛╤Б╤В╤М╤О 100 000 ╨┤╨╛╨╗╨╗╨░╤А╨╛╨▓ ╨б╨и╨Р ╤Б╨╛ ╤Б╤А╨╛╨║╨╛╨╝ ╨┐╨╛╨│╨░╤И╨╡╨╜╨╕╤П 4 ╨│╨╛╨┤╨░. ╨Я╤А╨╡╨╛╨▒╨╗╨░╨┤╨░╤О╤Й╨░╤П ╤А╤Л╨╜╨╛╤З╨╜╨░╤П ╨┐╤А╨╛╤Ж╨╡╨╜╤В╨╜╨░╤П ╤Б╤В╨░╨▓╨║╨░ ╤Б╨╛╤Б╤В╨░╨▓╨╗╤П╨╡╤В 10%.

╨б╨╗╨╡╨┤╨╛╨▓╨░╤В╨╡╨╗╤М╨╜╨╛, ╤Ж╨╡╨╜╨░ ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╕ ╤А╨░╤Б╤Б╤З╨╕╤В╤Л╨▓╨░╨╡╤В╤Б╤П ╨┐╨╛ ╨┐╤А╨╕╨▓╨╡╨┤╨╡╨╜╨╜╨╛╨╣ ╨▓╤Л╤И╨╡ ╤Д╨╛╤А╨╝╤Г╨╗╨╡ ╤Б╨╗╨╡╨┤╤Г╤О╤Й╨╕╨╝ ╨╛╨▒╤А╨░╨╖╨╛╨╝:

• ╨ж╨╡╨╜╨░ ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╕ = 68 301,35 ╨┤╨╛╨╗╨╗. ╨б╨и╨Р ~ 68 301 ╨┤╨╛╨╗╨╗. ╨б╨и╨Р

╨Ш╤Б╨┐╨╛╨╗╤М╨╖╨╛╨▓╨░╨╜╨╕╨╡ ╨╕ ╨░╨║╤В╤Г╨░╨╗╤М╨╜╨╛╤Б╤В╤М

╨Ъ╨╛╨╜╤Ж╨╡╨┐╤Ж╨╕╤П ╤Ж╨╡╨╜╨╛╨╛╨▒╤А╨░╨╖╨╛╨▓╨░╨╜╨╕╤П ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╣ ╨╛╤З╨╡╨╜╤М ╨▓╨░╨╢╨╜╨░, ╨┐╨╛╤Б╨║╨╛╨╗╤М╨║╤Г ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╕ ╤П╨▓╨╗╤П╤О╤В╤Б╤П ╨╜╨╡╨╛╤В╤К╨╡╨╝╨╗╨╡╨╝╨╛╨╣ ╤З╨░╤Б╤В╤М╤О ╤А╤Л╨╜╨║╨╛╨▓ ╨║╨░╨┐╨╕╤В╨░╨╗╨░. ╨в╨░╨║╨╕╨╝ ╨╛╨▒╤А╨░╨╖╨╛╨╝, ╨╕╨╜╨▓╨╡╤Б╤В╨╛╤А╤Л ╨╕ ╨░╨╜╨░╨╗╨╕╤В╨╕╨║╨╕ ╨┤╨╛╨╗╨╢╨╜╤Л ╨┐╨╛╨╜╨╕╨╝╨░╤В╤М, ╨║╨░╨║ ╨▓╨╡╨┤╤Г╤В ╤Б╨╡╨▒╤П ╤А╨░╨╖╨╗╨╕╤З╨╜╤Л╨╡ ╤Д╨░╨║╤В╨╛╤А╤Л ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╕, ╤З╤В╨╛╨▒╤Л ╤А╨░╤Б╤Б╤З╨╕╤В╨░╤В╤М ╨╡╨╡ ╨▓╨╜╤Г╤В╤А╨╡╨╜╨╜╤О╤О ╤Б╤В╨╛╨╕╨╝╨╛╤Б╤В╤М. ╨Я╨╛╨┤╨╛╨▒╨╜╨╛ ╨╛╤Ж╨╡╨╜╨║╨╡ ╨░╨║╤Ж╨╕╨╣, ╨╛╤Ж╨╡╨╜╨║╨░ ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╕ ╨┐╨╛╨╝╨╛╨│╨░╨╡╤В ╨┐╨╛╨╜╤П╤В╤М, ╤П╨▓╨╗╤П╨╡╤В╤Б╤П ╨╗╨╕ ╨╛╨╜╨░ ╨┐╨╛╨┤╤Е╨╛╨┤╤П╤Й╨╡╨╣ ╨╕╨╜╨▓╨╡╤Б╤В╨╕╤Ж╨╕╨╡╨╣ ╨┤╨╗╤П ╨┐╨╛╤А╤В╤Д╨╡╨╗╤П, ╨╕, ╤Б╨╗╨╡╨┤╨╛╨▓╨░╤В╨╡╨╗╤М╨╜╨╛, ╤П╨▓╨╗╤П╨╡╤В╤Б╤П ╨╜╨╡╨╛╤В╤К╨╡╨╝╨╗╨╡╨╝╨╛╨╣ ╤З╨░╤Б╤В╤М╤О ╨╕╨╜╨▓╨╡╤Б╤В╨╕╤А╨╛╨▓╨░╨╜╨╕╤П ╨▓ ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╕.

╨Т╨╕╨┤╨╡╨╛ ╨╛ ╤Д╨╛╤А╨╝╤Г╨╗╨╡ ╤Ж╨╡╨╜╨╛╨╛╨▒╤А╨░╨╖╨╛╨▓╨░╨╜╨╕╤П ╨╜╨░ ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╕

╨а╨╡╨║╨╛╨╝╨╡╨╜╨┤╤Г╨╡╨╝╤Л╨╡ ╤Б╤В╨░╤В╤М╨╕

╨н╤В╨╛ ╤А╤Г╨║╨╛╨▓╨╛╨┤╤Б╤В╨▓╨╛ ╨┐╨╛ ╤Д╨╛╤А╨╝╤Г╨╗╨╡ ╤Ж╨╡╨╜╨╛╨╛╨▒╤А╨░╨╖╨╛╨▓╨░╨╜╨╕╤П ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╣. ╨Ч╨┤╨╡╤Б╤М ╨╝╤Л ╨╛╨▒╤Б╤Г╨╢╨┤╨░╨╡╨╝, ╨║╨░╨║ ╨▓╤Л╨┐╨╛╨╗╨╜╤П╤В╤М ╤А╨░╤Б╤З╨╡╤В╤Л ╤Ж╨╡╨╜ ╨╜╨░ ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╕, ╨┐╤А╨░╨║╤В╨╕╤З╨╡╤Б╨║╨╕╨╡ ╨┐╤А╨╕╨╝╨╡╤А╤Л ╨╕ ╨╖╨░╨│╤А╤Г╨╢╨░╨╡╨╝╤Л╨╡ ╤И╨░╨▒╨╗╨╛╨╜╤Л Excel. ╨Т╤Л ╨╝╨╛╨╢╨╡╤В╨╡ ╤Г╨╖╨╜╨░╤В╤М ╨▒╨╛╨╗╤М╤И╨╡ ╨╛ ╤Д╨╕╨║╤Б╨╕╤А╨╛╨▓╨░╨╜╨╜╨╛╨╝ ╨┤╨╛╤Е╨╛╨┤╨╡ ╨╕╨╖ ╤Б╨╗╨╡╨┤╤Г╤О╤Й╨╕╤Е ╤Б╤В╨░╤В╨╡╨╣:

• ╨Ъ╤Г╨┐╨╛╨╜╨╜╨░╤П ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╤П
• ╨Т╤Л╤З╨╕╤Б╨╗╨╕╤В╤М ╨▓╤Л╨┐╤Г╨║╨╗╨╛╤Б╤В╤М ╤Б╨▓╤П╨╖╨╕
• ╨Ю╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╕
• ╨б╤А╨░╨▓╨╜╨╕╤В╨╡ ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╕ ╨╕ ╨┤╨╛╨╗╨│╨╛╨▓╤Л╨╡ ╨╛╨▒╤П╨╖╨░╤В╨╡╨╗╤М╤Б╤В╨▓╨░