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How much should be deposited into an account today if it is to accumulate to $\$ 15,000 dollars in 10 years if the account bears interest at $6.25 \%$ compounded(a) monthly, (b) daily, (c) continuously?

(a) 8041.95(b) 8029.35(c) 8028.92

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 3

The Number $e$

Oregon State University

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Lectures

03:00

How much should be deposit…

02:46

03:09

01:56

How much must be invested …

01:28

How much must beinvest…

00:38

How much money must be dep…

$\$ 1250$ is deposited int…

01:13

Compound Interest A deposi…

04:05

If $\$ 12,500$ is invested…

12:50

(a) A bank account earns $…

eso We're still using the compound interest formula, but the difference now Oops. Forgot my end in there. E to the r t for compounding continuously. That was for this one is now there's a goal in mind like you wanna end with the dollar that they give you so to solve for the principal. What? You need to start with us to divide over e to the RTs. The same thing with this one, which is actually I need to do first if I want to solve for the principal what we're starting with you take the ending imbalance that they tell you and you divide by one plus r over and to the NT power. Now, depending on how good you are with the calculate, you might have to put in parentheses in there to get the right answer. So, in part, A, since I already sold for it, I'm gonna go ahead and say, Okay, well, if we want to end with $15,000 then you divide by that formula, that one plus r, which they tell you, is 6.25%. So change that to a decimal. Okay. Divided by or doing monthly so maybe I should write that down. Well, monthly means that we need 12 compounding per year to the 12 times we're doing this in the course of 10 years. You might need to put this in parentheses as well, depending on your calculator. But as you take that in your ending amount or excuse me should be your starting amount needs to be 80 41 95 8000 $41.95 Little dollar Sign in there for you. Eso What's different between that and daily? Well, the number of compound ings change. It's still 15,000 the goal that you wanna have in 10 years. But the difference is you take that 0.6 to 5 and instead of compounding 12 times years, compounding 365 times a year. And make sure you figure out how to use your calculator. If you need to put parentheses in here, then do it. Or if you need to put parentheses here, then do it. And what you'll find out is you don't need as much money to get that that much $8029 because it's compounding more often and 35 cents. We'll get you up to $15,000 in 10 years, and then the last one is continuously. You know, that's the perk formula hopes continuously on That's taking that 15,000 the ending balance and dividing by e the 2.718 number we've talked about, uh, to the 0.6 to 5 times 10 power. And again, depending on how your calculator works, you might need to put in some parentheses in there. Um, you know, to make sure you get the right answer. Still in the 8000 range, But only $28.92. We'll get you up to that amount. So there you have it.

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