Question 698913

Hi. I kind of understand how a total salary amount over a certain period of years with a fixed annual increase using arithmetic series is done but how does one do this if the annual rate of increase is a percentage?  e.g. What would be the total amount of a salary that starts at $20,000 per year at an annual increase of 5% over 10 years? Thank you. Paul Stone


This is the equivalent of asking one to determine the future value, after 10 years, of $20,000, which is compounded annually, at a rate of 5%.


The future value formula, {{{A = P(1 + r/m)^(tm)}}} can be used, with A being the future value, or value after 10 years, P = present value, or $20,000, r = rate of interest, or 5% (.05), m being the amount of compounding periods per year, and t being the time, in years (10)


Therefore, {{{A = P(1 + r/m)^(tm)}}} becomes:


{{{A = 20000(1 + .05/1)^(10 * 1)}}} ----- {{{A = 20000(1.05)^10}}}


A, or amount in 10 years = 20000(1.628894627), or ${{{highlight_green(32577.89)}}}


You can do the check!!


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