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For how long must $\$ 700$ be left on deposit at $6 \%$ compounded monthly to reach a total accumulation of $\$ 1750 ?$

$$15 y 3 m 22 d$$

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

02:50

For how long must $\$ 1700…

03:20

For how long must $\$ 900$…

01:13

Find how long it takes $\$…

03:16

For how long must $\$ 2200…

03:32

How long will it take to e…

Okay, so we're using the formula. And every teacher kind of uses slightly the same slightly different, um, formulas like this. But since we are, uh, taking a $700 that's your principle, P, um, they tell you what the rate is 6% now, make sure you change 6% to be a decimal by divided by 100. We're compounding monthly, so that means and equals 12. There's 12 months in a year. We don't know the amount of time, and all we know is that we want to end up with a total of 17. 50. It's kind of a step by step process to solve this. We're gonna divide 701st. And, uh, your next step is just to log or natural log either side. Um, I like to hit the log button, although I know lots of teachers that like to do the natural log. But anyway, the reason for that is, then you can move the exponents in front. So we're looking at 12 tee times log. Yeah, of that number. Okay. Okay. Okay. And so, if I'm solving for tea, kind of getting to my answer here. It's a giant multiplication problem. So all I have to do is log of that 17 50 over 700 divided by, uh I mean divided both the 12 and the log of that one plus 10.0 6/12 eso as I go to my calculator and type that in divided by 700. Uh, I'll buy. I should put it all in parentheses. 12, Because make sure you type into your calculator correctly and your calculator does the order of operations, so if you don't type it incorrectly, you will get the wrong answer. So the decimal that you get is 15.310 Um, but it looks like I'm gonna circle that because that is good. So that would be 15 years, and then some change. Well, how you can change it to the number of months or days. Yeah, because it wants you to convert is take the truncated, So subtract off the 15. So this is sort of additional work. So you're just looking at that 150.310 numbers. And if you multiply that by 12 because there's 12 months in the year, you get this decimal of 3.716 so that tells me is that that would be three months. But then, if I truncate that number again, I'm going to go back to Blue. I only look at the 0.716 number and I multiply that by it would be the number of days in a month. So I don't know if you're just assuming 30 days in a month, but some months have 31 days. Uh, let's see if I do times 20 times 38 21 a half days. If I do Times 31 it's 22.2 days, so I don't know how Whether you should say 21 or 22 days, um, depends on what number you're multiplying by. You know, if you multiply by 30 you get the top one. But if you multiply by 31 you get the bottom eso. I don't know what the answer would be better of. That's up to you, I guess. Or your teacher, for that matter.

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