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AS 2053 (10)
Chapter 4

# Actuarial Science 2053 Chapter Notes - Chapter 4: Sug

Department
Actuarial Science
Course Code
AS 2053
Professor
Steven Kopp
Chapter
4

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Annuities Where Payments Vary
(section 4.4)
Not all annuities have a level series of
payments; instead we are going to look at
annuities where the payments change every
period
Two Standard Types
(I) Payments vary in terms of a constant
ratio
these are annuities where payments
change by a certain % every period
(II) Payments vary in terms of a constant
arithmetic difference
these are annuities where payments
change by a certain dollar amount
every period

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(I) Payments vary in terms of a constant
ratio
These type of problems are best solved by
using basic principles:
draw a time diagram and choose a focal
date
write out the first few terms of the
equation of value
solve using the sum of a geometric series

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Example 4.4.1
A man, age 35, is injured in a car accident and is
no longer able to work. He sues for damages
and is awarded a lump sum of money equivalent
to his future lost income. He is currently
earning \$35,000 a year, has 30 years until
retirement and is expected to get a raise of 3%
per year. If j1 = 6%, what would be the lump
sum award? (assume wages are paid in one
lump sum at the end of the year).