常用公式大全edu-exam-fm-notation-term(SOA北美精算师考试handbook notes).pdf

Notation and terminology used for Exam FM/2 The following notation and terminology will apply to the examination questions. Unless otherwise stated in the examination question, rates are expressed as annual rates. For example,: the rate of interest, the rate of discount, the force of interest, the yield rate, and the coupon rate. The effective rate of interest is denoted by i. The nominal rate of interest payable m times per period is denoted by i(m). When more than one interest rate is referenced in a question, additional letters such asj may be used to denote the additional interest rates. i The effective rate of discount is denoted by d and is equal to . The nominal rate of discount payable 1+i m times per period is denoted by d(m). 1 The discount factor is denoted by v and is equal to . 1+i Force of interest: A constant force of interest is denoted by δ A force of interest varying by time is denoted by δt Current Value: The current value, as of a given date, of a set of cash flows is equal to the accumulated value of the cash flows occurring prior to the given date plus the discounted value of the cash flows occurring on or after the given date. The term “present value” is used when all cash flows are discounted and the term “future value” is used when all cash flows are accumulated. An annuity-immediate is an annuity where the payments are made at the end of each period. The present value of an annuity-immediate with n payments of 1, at interest rate i, is denoted by a or a n n i The accumulated val