Question 1085929

A man's salary started with $7,500 for the first year and increase by $750 each year up to a maximum of $15,000 per annum at which it remains constant. Find his total earning in his thirty years of service. 
<pre>Ask yourself, "How long after starting will it take him to make the maximum of $15,000?
With T being time (in years), we get: T * 750 + 7,500 = 15,000 =======> 750T = 15,000 - 7,500 =====> 750T = 7,500 ======> {{{matrix(1,8, T, or, time, "=", "7,500"/750, "=", 10, years)}}} 
Now, use the formula for the sum of an AP: {{{matrix(1,3, S[n], "=", (n/2)(2a[1] + (n - 1)d))}}} to get the amount earned 10 years after starting. This should give you: $108,750
From years 11 - 30 (20 year span), he would've earned 20(15,000), or $300,000.
Adding the 1st 10 years' earnings to the last 20 years' earnings, we get: {{{highlight_green(matrix(1,8, "30-year", earnings, of, "$108,750", "+", "$300,000", "=", "$408,750"))}}}