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If $\$ 3000$ is invested at 5$\%$ interest, find the value ofthe investment at the end of 5 years if the interest iscompounded(a) annually(b) semiannually(c) monthly(d) weekly(e) daily(f) continuously

a) $$\$ 3828.84$$$$\$ 3840.25$$b) $$\$ 3840.25$$c) $$\$ 3850.08$$d) $$\$ 3851.61$$e) $$\$ 3852.01$$f) $$\$ 3852.08$$

Calculus 1 / AB

Chapter 3

INVERSE FUNCTIONS

Section 4

Exponential Growth and Decay

Derivatives

Differentiation

Applications of the Derivative

Missouri State University

Harvey Mudd College

Idaho State University

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Hey, guys, welcome back. We're told that we have initial investment of $3000 at 5% interest. We were asked to figure out how much said investment will grow at different interest annual interest. Semiannual monthly, weekly daily. Continuously. We'll use our equation. Our amount after sometime is able to our initial amount our initial amount being the 3000 plus our rate over end over end to the team and r T. It's how many years. So in this case, he would be five for all these things two years ago to five. And then end is how many times per year times per year. So first we were asked to figure out what happens. It's calm, pounded annually, so his compound annually than end is simply one part a and his one I have 3000 one plus r ever end are is 0.5 Number one raised to the end T and we said was one t value is five. And if you do the math, that comes out to 3000 828 0.84 Next problem. Rest figure. What happens if this compound id semi annually? So for semi annually than end will be equal to two. I will say that a city should have said That appears well. A city is equal to 3000 one plus 10.5 and is not to times that by to to the five. And that will give us a value of 3000 140 0.25 Next, we're asked to figure out what happens if it's calm. Pounded monthly 12 months and years and his 12 and we have a He is evil Toe 3000 one plus 10.0 5/12 0 5/12 I replied by two times 12 and that comes out to 3000 850 0.0 eight. Next to ask to figure out what happens if it's compound ID weekly in its weekly. There are 52 weeks in a year, so our equation becomes. Eight of the tea is equal to 3000 3000 one plus 10.5 over 52 multiplied by 52. I'm sorry. I apologize up here. I had a slight mistake. Our experts should have been 12 multiplied by five and this answer is still correct. That was the correct answer. Going back now. Down to Part D. You do this math? Get a value of 3000 851 0.61 now for part, you were asked for your what happened to his compound it daily. There are 365 days in a year. To me, it's not only beer, we'll have a Sebti people of 3000 one plus 0.5 3 65 raised to the five years times 365 times every year. If you do the math on that one, that comes out to 3000 800 3000 800 52 $01. Part of the rest of you know what happens. It's compound to continuously. Basically, we're saying what happens when N goes to infinity or any ghost Infinity, Our equation turns into a city is ableto our initial value. Times e. Raised to the rt becomes 3000 times E Raised to the are just 0.5 times T just five, and that comes out to three 1000 800 to point a sense. Now it's part F that includes parts A through F, and that includes the problem. Thanks for watching

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