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How long would it take for an investment to (a) triple; (b) quadruple, earning $8 \%$ compounded continuously?

(a) $13 y 8 m 24 d$(b) $17 y 3 m 29 d$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 6

Properties of Logarithmic Functions

Missouri State University

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

06:07

(a) How long does it take …

04:51

06:37

05:14

How long will it take for …

03:49

I'm starting this problem right after, uh, the previous problem because you're still using that pert formula P e to the rt eyes equal toe A. The thing is, is if you're trying to triple your money so this value needs to be three times the initial amount P e to the r t. So if we're tripling that number and we want Thio, you know, solve it doesn't matter what your starting balances, because the peace will cancel and the process will always be to natural log both sides because that will cancel out with the ease and then to solve for t you divide by the interest rate. Well, the interest rate in this problem is 0.8 because it's 8% eso. I hope that makes sense. Then, uh, if we're trying to quadruple our number Well, what's different there for quadrupling is this would be four yada yada. Uh, so if you look at my work, I think it makes perfect sense that you would do natural log of forward, divided by 0.8 is equal to t eso. As you type that into your calculator, both answers and it doesn't really matter which one. You do, uh, for tripling your number. That would be about 13.733 as you change that. So that's years. That's about 13 years, you know, and you and you truncate your numbers and multiplied by 12, you will get eight months and then truncate that number and multiply by 30 and then round up. You get about 24 days, whereas should be circling that in green. There you go. That's the first part. And part B changed that natural log of three to be natural log of four and you get an answer of 17.3 to 9. So that's 17 years. And maybe this time I'll actually show you how you truncate you. Take that 0.3 to 9. So take away that 17 and you multiplied by 12 because there's 12 months in a year. Um, okay, you get 3.944 Yes. Okay, so that says that that is three months. But if you truncate again, so you just look at that. 0.944 multiplied by 30 because the roughly 30 days, uh, any a month what you get 28 some change. But the argument would be that you don't have it on the 28th day. You gotta wait till the 29th day before you finally have that money. So this is a very rough estimate. 29 days. Eso You could repeat the process to get this answer as well.

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