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How much should be deposited into an account today if it is to accumulate to$\$ 2100 dollars in 7 years if the account bears interest at $5 \%$ compounded (a) monthly, (b) daily, (c) continuously?

(a) 1480.92(b) 1479.88(c) 1479.84

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 3

The Number $e$

McMaster University

Harvey Mudd College

University of Michigan - Ann Arbor

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So the whole premise of this problem is understanding the, um, compound interest, which is this formula. Uh, and if you're compounding continuously, that just changes over to this form of P E to the R T. So as they are answering, the question is they want the ending amount so they know the ending amount. They're asking how much you need to start with now. Notice how I set this up is a solve for the initial amount. You want to divide that piece over on? Same thing on this one. Pretty straightforward, because it's multiplication problem. Um, when we get to let her see, so all you have to do her part? A. The monthly amount is to recognize that. Okay, we have, um 2100. Yeah, that's how much we want to end with our interest rate. They tell us is 5%. Now, make sure you change the rate to be 0.5 Otherwise, the formula won't work. There's 12 months in a year. So and it's 12, um, on Ben 12 times. We want this in seven years. Now, you might need to figure out how to use your calculator because some calculators make you put parentheses around here. Here, here. Lots of parentheses. But the answer. You should come up with this 14. 80 92. What? Yeah, $1480. 92 cents. And that answer should make sense in about seven years. You know, you might get an answer pretty close to that. So then let me move down. And the only difference for part B is now we're doing this daily, uh, 2100. All of this is the same again. You might need to pay attention to your calculator. Uh, the differences. There's not 12 days in the year. There's 365 days a year to the 365 times. 12 times seven. Excuse me, Power. Um, And this time you only have to put in 14, 79 88 which I would anticipate because, um, hell, compounding daily means you'll make more money so you can invest less. Hopefully, that makes sense. And then when you see continuously, uh, for part C, you're taking that 2100 Still, But this time you're divided by the number E to the 0.5 times seven power and again double check your calculator. Make sure you know how to use it. Um and you should Onley have to put in 14 79 84. So you get to save four pennies if you do it that way. There you go. There's your three answers A B C.

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