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What interest rate compounded continuously did a $\$ 1500$ investment earn if it accumulated to $\$ 4500$ in 18 years?

$$6.10 \%$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 6

Properties of Logarithmic Functions

Missouri State University

Campbell University

Harvey Mudd College

Baylor University

Lectures

02:04

What interest rate compoun…

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01:47

01:14

If an investment triples i…

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If an investment triples…

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assume that there are no d…

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Assume that there are no d…

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If the present value of …

Continuous compound intere…

Yeah. So the moment you see compounded continuously, you want to use your pert formula e to the r T power, and, uh, we want to get $4500. Okay, if we had 1500 to start with, uh, he is just a number. That's not gonna change. We don't know the rate, but we have 18 years, so replaced tea with 18 eso. It's always the same process to solve this problem, divide the principal over, and, uh, this actually simplifies really nicely toe exactly three. So we're essentially asking when are we tripling our money? Our next step is to undo E by taking the natural log on both sides. And the reason why this is what we want to do is because then we could take this power, move it in front. So we're looking at 18 are on natural log of e cancel each other out because natural of e is one, and then the soul, for the rate you divide by 18 because it's a multiplication problem. So just go to your calculator type of natural. Guthrie, close your princess Stephanie Toone, divided by 18. Now, remember, this gives you a decimal 180.61 034016 And to change it back to a rate, a percent? Yeah. You know, multiplied by 100 eso you're looking at 6.103%. I like three decimals, and so do a lot of math teachers. Yeah.

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