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10) it take an A high-yield initial savings investment of $2500 to pays 8% interest; 1 compounded 1 continuously_ How long ` would...

Question

10) it take an A high-yield initial savings investment of $2500 to pays 8% interest; 1 compounded 1 continuously_ How long ` would

10) it take an A high-yield initial savings investment of $2500 to pays 8% interest; 1 compounded 1 continuously_ How long ` would



Answers

If
12,000 is deposited in an account paying $8 \%$ interest per year, compounded continuously, how long will it take for the balance to reach $\$ 20,000 ?$

In this question. We're told that $100 is invested at 8% for here and come about a month week and were asked how long it will take before the amount is $150. So we know right away they were going to use the compound interest for where a represents the amount after tea. Number of years. He's the principal investment and this number of compounds. He's a number of years and are straight of interest. So we know that our is 8% which is Lynch is your your eight to you. So we're trying to calculate and is 12 points was compounded monthly. Andi P is 100 others. Instance the questions asking us to find our way to get $150 and result on Mt. So the first step is going to be to plug all this data in two our equation both. So 150 is equal to 100 times one plus you put you ate over of their power, us 12. Now we're just gonna do some simple algebra and South three D. So the first step is gonna be to divide 200 over so 15 is equal to book this into a calculator. You get 1.6 one point. Use you 667 to the power of 12. T 12. No, just take Ellen. Isolate the T l N 15 Well, then year 0667 are 12 g. You can bring the 12 t to the front, so 5 to 12 T brackets learned of one point. Use your six. Except so now we're gonna divide Ln of 1.5 by 12. Ellen one ensures your 667 isolated teeth. T is equal to Ellen. 15 Hopes over 12 Helen. One point Use your 66 So get tea is equal to 58 years. 5 22 Hey, five years. That's the first question now in the second part of the question asked how long it will be compounding was to be continues. So for compounded continuously, we know that the formula well look a little different from the a p e to the power for chief. Raise them out after two years peace, the principal amount of investment. He's constant, interesting tes a number of years, so again result for teeth. So You know, the mound fifties is just playing the same values. Physical 200 Heath are Cheapens your eight cheek. This is okay again. We're just gonna divide the 100 over one. Put five physical e bars. You hate team. I was just gonna take Ellen. Canceled e So for tea? Sure. Eight. You get 1.5 is equal to your parents. You hate cheese. T tell 58 which is equal to five you 68 years. That is for the second part.

For this problem we have $10,000 deposited in a money market fund. So our amount as a function of X. Or time is going to be 10,000 um Times E. To the R. to the rate is going to be 0.08%. So 8% 0.08. As compounded continuously. So we want to know how much interest will be earned during the second your of investment. Um so we have X. Here. So we see that a of one if you look at A. F. Q. That gives us 11,000 Um 735, that just tells us how much we have in the account. But what we actually want to do is subtract that by how much we had the first year, How much we made the first year. And we see that from that time We actually made 902 $24. So remember to subtract the first year because that will tell you how much you've made in the second year. Mhm.

Okay, so we're given How long does it take to earn 1000 and interest on the deposits of 6000 at 8% compounded continuously. So we have our formula A single toupee, E R nt. No, we're asked, How long does it take to earn one? That was an inch an interest on a deposit of six Teligent stop Means we have, um, 6000 plus 1000 which means that our annual is 7000. Our principal is six. Downs is and our rate is point 0/8. I'm plugging in. Everything we know get 7000 is equal to 6000 um, times e sort of 0.8 t. So we have 7/6 physical Tito points. You're 80 taking eligible science, we get the following and now T is equal to Ellen of 7/6, divided by 0.0 AIDS, which is equal to 1.9 years

The question asked to find how long it would take for $1000 to double as a percent compound and continuously, we sought out by knowing the equation for a comp I interest compound and continues interest rate, which is a equals p times E to the power of RT A is our future value P is our principal amount or are deposited amount. Our is our interest rate in decimal form 20 is amount of years. For this problem, P would be $1000 our principal amount or deposit amount our would be our interest rate 8% or in decimal form, 0.0 for a our future value. We want $1000 to double. So $1000 times two is 2000. Our goal is to find t. So what we want to do is to isolate T. So what we can do is divide a by P. Then we can find the natural log on both sides and we want to do this because the natural log of E to some power of expo equals X. So now the equation becomes Ln of a overpay equals r t, then we could multiply our I'm sorry we couldn't divide our by both sides. And we get Ellen of a over p divided by R. So now that we have an equation for tea, we can plug in the variables. So, Alan, of a $2000 divided by P $1000 all over our is your 0.8 to simplify will have Allen of two divided by zero points your eight or just 8.6 years.


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