PreCalc/Calculus help!
Calculus

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Determine the amount of money that should be invested at a rate of 6.5% compounded monthly to produce a final balance of $15,000 in 20 years?
Well, I don't know if I can get you an exact or correct answer, or even an answer at all. But I will try:
So the total number of months would be 20 X 12= 240
So your getting a 6.5 percent interest for 240 months.
If you can imagine what an equation would look like, you can get there by saying that your final balance is equal to your initial investment plus 6.5 percent of your initial investment times 240. (i think that's how investing works, because if you have to reinvest money every month, then this answer will be completely wrong) But if you take those words into a written equation it looks like this:
15,000= x + ((x*.065) X 240) The reason there is a .065 instead of a 6.5 is because if you were to convert 6.5 into a fraction, an multiply, then you are really multiply that number by 6 and one half. That's big. This percent is small, so it has to be smaller. 6.5 is 6.5 percent of 100. You are dealing with numbers that stand alone, they aren't fractions. so you need 6.5 percent of 1. To get from 100 to one, you move the decimal over 2 spaces. So to get from 6.5 percent of 100 to 6.5 percent of 1, you move that decimal over too to get .065.
But let's switch it so it looks like this:
15,000= x + 240(.065x)
Which if you distribute turns into 15,000= x +15.6x
If you didn't already know, multiplication is the same thing as adding repeatedly: So 4 X 3 really just means 4 plus 4 plus 4 plus 4. (4 with a 4 added to it two more times.) I promise this is relevant. Since 4X3= 12, then 4+4+4= 12. If you have an equation like this: 3x and just to keep it the same, let's say x equals 4. Then the equation is really 3X4, but it looks like 3x.
That being said if you have x + 3x, and x equals 4, then what you really have is 4 + (3X4) Which is 4 + 12, which is 16. That's the same as saying 4x, (which would look like 4X4). That's why you can add two variables, if they are both the same, even if there's a fraction in the front, even if there's a decimal, or a huge number, or no number, or a negative.
In short: If you have (anything)x + (anything)x, you can add them to get (anything+anything)x.
So now to bring it all back, if you have 15.6x + x, you really have 16.6x.
And now you solve for x.
15,000=16.6x
15,000/16.6= x
15,000/16.6 equals 903.61.
Plug it back into the original equation to check it:
(903.61) + 240(903.61*.065) You should get 15,000.
If you put it in exactly like that, your final number is 14999.926, which rounds up to 15,000.
I don't know if I've made this easier or harder, but I hope it helps. If you need any help in the future, email me: doctorturner1@gmail.com I'd love to help you learn math, I might even learn something myself. No charge at all. No catch.
If not, let me leave you with this. While math may seem very complicated, all of it can only exist because of very simple principles of addition, subtraction, division, and multiplication. Everything else is just different words, and applied to different things, but all of the conclusions can be reached logically. Math always adds up.
All you have to do, is rephrase it so you understand what it's really asking (especially in New Math), and use what you know. But if you have a hard time, and don't get everything right, no worries.
You will be just fine out in the "real world". So don't sweat it, you aren't stupid. You are okay right where you are.
Email me if you'd like to continue your study. Thanks, and take care kiddo. :)
Doctor Turner
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