ACTSC231 Lecture Notes - Lecture 13: Geometric Progression, Linear Interpolation, Investment

• School: University of Waterloo
• Department: Actuarial Science
• Course: ACTSC231
• Professor: Keith Freeland

Document Summary

Let a opening balance at t 0. Let b closing balance at t 1. Let ctk net contribution at time tk, where. 0 t1 t2 tn 1. Let b balance at time 2, ctk cash flow at time tk, where 0 t1 tn 2. Consider 1 i 2 tk 1 i 2 tk this is a poor approximation when 0 tk 2. Instead use linear interpolation between 1 & 1 i 2. 1 i 2 t 1 j 2 t for some rate j such that we have equality at t 0 and t 2. Need 1 i 2 1 2j or 1 i 1 2j 1/2. 1 i m m m 1 i for any m 0. 1 i 2 t 1 i 1/2 2 t . B a 1 i 2 ct 1 i 2 t. A 1 i 1/2 2 ct 1 i 1/2 2 t .