Transcription of Financial Mathematics for Actuaries
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Financial Mathematics for Actuaries
Financial Mathematicsfor ActuariesChapter 2 AnnuitiesLearning Objectives1. annuity -immediate and annuity -due2. Present and future values of annuities3. Perpetuities and deferred annuities4. Other accumulation methods5. Payment periods and compounding periods6. Varying annuity -Immediate Consider an annuity with payments of 1 unit each, made at the endof every year fornyears. This kind of annuity is called anannuity-immediate(also calledanordinary annuityor anannuity in arrears). Thepresent value of an annuityis the sum of the present valuesof each :Calculate the present value of an annuity -immediate ofamount $100 paid annually for 5 years at the rate of interest of 9%.Solution:Table summarizes the present values of the payments aswell as their :Present value of annuityYear Payment ($) Present value ($)1100100 ( ) 1= ( ) 2= ( ) 3= ( ) 4= ( ) 5= Weareinterestedinthevalueoftheannuityatt ime0,calledthepresent value , and the accumulated value of the annuity at timen,called the future Suppose the rate of interest per period isi,andweassumethecompound-interest method applies.
2.2 Annuity-Due • An annuity-due is an annuity for which the payments are made at the beginning of the payment periods • The first payment is made at time 0, and the last payment is made at time n−1. • We denote the present value of the annuity-due at time 0 by ¨anei (or ¨ane), and the future value of the annuity at time n by s¨nei ...
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