<p>Hey Guys, I need a little help. I don't have my practice book with me, but here's the gist of the question.</p>
<p>Start with the $500. Every day, you increase that $500 by two percent. After 100 days, how much money do you have?</p>
<p>I know you can do this with summation, i'm just having trouble.</p>
<p>I also tried doing this with A=PeRt (like treating this as if it is an interest problem).</p>
<p>Can someone help?</p>
<p>Thanks!
JR</p>
<p>Let f(x)= your money after x days
f(x)=500.(1,02^x)
f(100)=500.(1,02^100)~500.7.25= $3625</p>
<p>in case u dont know where he got 1.02 ^ from, it's
.2 x 500 + 500 = price after day 1
in another words, it's 1.02 x 500. it'll give u the price directly~ [factoring the 500 works well too]
then it just keeps compounding....</p>
<p>A better formula would be A=P(1+r)^t.</p>
<p>islander4, what do those letters stand for?</p>
<p>^ P = the amount you started with
r = rate, so in this case it is 0.02 (2%)
t = time</p>
<p>For intervals of a month, year, week, etc, another formula has to be used. A=P(1+(r/i))^it. i represents the intervals of a certain period of time. Such as every quarter of a year, half-day, etc.</p>
<p>^ "Fun" Fact: as the time intervals get very small, the formula becomes A = Pe^(rt) ...</p>
<p>One definition of the number "e" is the expression (1 +1/n) ^ n as n gets very big (try it on your calculator for "fun") ....</p>
<p>You can find the formula yourself. It's just what you had the day before, plus 2 percent of it. Or in other words, what you had the day before multiplied by 1.02. </p>
<p>after n days:
0: 500
1: 500<em>1.02
2: (500</em>1.02)<em>1.02
3: ((500</em>1.02)<em>1.02)</em>1.02
...</p>
<p>So after n days, you have 500*1.02^n.</p>