This

**preview**shows pages 1-3. to view the full**15 pages of the document.**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).

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