if-2000-is-invested-at-an-interest-rate-of-35-per-year-compounded-continuously-find-the-value-of-t-2

Question

If $\$ 2000$ is invested at an interest rate of $3.5 \%$ per year, compounded continuously, find the value of the investment after the given number of years.
a. 2 years
b. 4 years
c. 12 years

Ankit Gupta · Accepted Answer

we are given indiscretion that our principal amount equals $2000. The rate of interest is 3.5% on its compounded continuously and the formalize B E a Stow Arthuis for A B and given time equals two years Onda. We plug all the values and to get amount as 2001. $45.2 for beat Me argument. But he equals four years. So we plug the equals two on, dressed Up for our values to get the amount as 2300.55 dollars. And for party, we are given that p equals 12 years. So we plug in all the given information in our form. Love, I&#x27;m get the amount as $3043.92.

Mitchell Vandel · Answer

already. So looks like we&#x27;re gonna be working on problem number 33 in chapter four. Section two, begin with. I&#x27;m just gonna go over what it is that I look at when I&#x27;m looking at these problems. So I will. Usually they&#x27;re highlight or at least pay attention to these different parts. Here&#x27;s so first, I&#x27;d noticed compound interest next. All 100 line, $2000 invested after that 3.5 percent interest per year. Next, compounding continuously. And lastly, I&#x27;d like to make sure I know what it is that we&#x27;re looking for is the answer of this equation, uh, of this question. And so for that we have that they&#x27;re asking for the value after a certain number of years, and so help me remember that. That&#x27;s the question. Will you put a question mark by it or I&#x27;ll circle? It helped me remember, uh, next we&#x27;re gonna have to figure out how we&#x27;re gonna solve this question and Howard to solve this problem in order to do so, you need to know which question ready? And so the way I kind of break this down is if compound interest to begin with. And so if I know that&#x27;s happening, and I know it&#x27;s gonna be some type of an equation using an exponents, and then the real key factor is going to be right here with our compounding continues. So for continuously, you only have one equation that&#x27;s gonna be focused on compounding continues. And that equation, yes, A of tea is equal to p time he raised to our times T. And so this equation will either be given to you on like a formula sheet or it&#x27;ll be also in your textbook, and it&#x27;s just gonna be the only equation that you&#x27;ll use to work on anything, work on anything that talks without compounding continuously. So once we get that, then next thing we&#x27;re gonna do is we&#x27;re going to, uh, we&#x27;re gonna separate out each variable and figure out what each of these air for have A of T and this is going to stand for our amount after two years or well, I think it is our end amount. Next, we have P, which is gonna be a principal or our start amount. Next, we have the letter E, which is this gonna be a constant and so it&#x27;s not gonna be a very boring. You don&#x27;t have to worry about plugging anything in for it. It&#x27;s just the number that going to use just like pie. It&#x27;ll be on your calculator. After that, we have our which is gonna be our rate. And you remember it could be in decimal form, not in percentage forms. Just take your percentage and divided by 100 in order to get into a decibel. So 3.5% will, actually instead, the 0.35 and then lastly, we have Ah, no, sorry. The Value t and this is gonna stand for years. So once we have all the variables figured out next you&#x27;re gonna connect these variables to the numbers that we&#x27;ve been given. So are $2000 invested. If we&#x27;ve already invested it, that means it&#x27;s our starting amounts that&#x27;s gonna make it R p or principle. After that, we have are 3.5%. That&#x27;s gonna be our rate. But remember, we&#x27;re gonna change it to a decimal point 0.0 35 instead. And then after that, we have our value after blankie years, which to me, I read as our end amount until we have it other end amount. That&#x27;s gonna be a ah key. And then the years is going to be given to us on each of the three sections of the problem. So for Section A, we want a of t on one time equation, which it already is. That&#x27;s good extra employees in our principle, which was $2000. Multiply that by he raised to R R, which is 0.0 35 multiplied by our years. Which is gonna be to in this case, then, once you put all that in your calculator, make sure that, um sometimes the calculator can get a little mixed up with parentheses and things like that. Sometimes after you do e rays to you can always put both of these in one big center. Parentheses help make sure gets entered correctly, Um, but as long as you make sure that&#x27;s working on your cake calculator than your good and when you put it in, you&#x27;ll get 2000 $145 and to set, I&#x27;m stopping at two decimal places, talking about money here. So usually money stops after two sets. Next, we&#x27;ll move on to Part B into The nice thing about this is all that&#x27;s gonna stay the same. The only part that changes is gonna be your years. So what we can do? We can take all of this. They&#x27;ll copy on down here, and the only part that&#x27;s gonna change. Like I said, the years you&#x27;re gonna change to four. And so when you put that in your calculator, you&#x27;ll get 2000 300 and 50 $5 then for the last part for part C. Same thing you&#x27;re going to get be able to copy over all this again, bring it down and just change the number of years of the end, which in this case is gonna be 12. Brought that a little bit big, but it&#x27;s still up in that exploded spot next to the 0.35 And when you enter that in your calculator, you&#x27;re gonna get out 3000 45 dollars and 90. So the answer&#x27;s two parts A, B and C or these $3 amounts here because those are the amount of money you&#x27;ll have after tea years at the end

Joseph Lentino · Answer

in this problem. We&#x27;re looking at compound interest. We&#x27;re told that we have $2000 to invest in a bank account. We also know that the interest rate will be 3.5%. Remember, 3.5% is the same as 20000.35 written as a decimal, and we&#x27;re compounding it continuously, which means we&#x27;re working with the formula. A of T is equal to hurt. The principle Here is my $2000. He is a number. My rate is 0.35 and the time is what we&#x27;re going to be evaluating this based upon. So in this case, the first problem we want to do is we want to evaluate what happens after two years. So when I substitute to into this form law, I have 2000 e to the 0.35 times two, and that will tell me after two years we will have $2145.2 in the bank account. Then we want to know what happens after four years. What would the amount be after four years? So we&#x27;ll substitute for in for tea and find out that there would be $2300.55. Finally, we want to know what would have didn&#x27;t happen after 12 years. So we plug in 12 30 and we will end up with $3043 in 92 cents. These would be the

Ankit Gupta · Answer

So the question $500 is invested at an interest rate off 3.75%. But here compounded quarter T. We have to find a value investment after the given number of years. So the formula for finding it amount is equal to be into one plus r, divided by N whole. Respond empty. But he is the principal amount being invested artist The interest rate in decimal and is the number of times and justice compounded. But yet and he is the number off years. So, according to the question, is 1/4 to 500. Art is equal to 0.375 and is it will do fourth because the interest has been compounded. Courted Lee, hence in part 80 is a Quito bunion. So even be Quinto 500 into one plus 0.375 Do I bite force hold a spot for and the one So this is coming out to be 519.0 and $5 in part, B T is equal to two years. Therefore it will be equal to 500 into one plus 0.375 hold a spot for divided by four whole race but foreign toe to which is eight. So this is coming off to be 538. 175 daughters in flight seat. The time is equal to three years. Sorry is this 10 years in part C, so 10 years hence alone will be equal to 500 into one plus 0.375 divided by four whole days. But for Internet, which is 40 so this is coming out to be 726.2 to $6.

Ankit Gupta · Answer

Ocean says that if $10,000 is invested at an interest rate off, 3% bloodier, compounded semi annually, find the value of investment after the given number off years. So the formula for finding this amount is equipped to be in tow. One plus R divided by entries but empty their peace. The principal amount are is the date and decimal, and it&#x27;s the number of times interest is compounded, buddy it and he is the number off years. According to a question. He&#x27;s a quick 10,000. Art is equal to three person, so it would be 0.3 since the interest is being compounded semi annually and will be equal to don&#x27;t. So we are given the value off key and we have to find uncertain what each value So in part eighties 1/4 to 5 years. Therefore able be quick, dude, 5000. Ah, sorry. This is 10,000 years. 10,000 into one place, 0.3 Do right by two days. Part goingto five my Justin. So therefore this amount is equal to 11,605 $0.4 in part B is equal to 10 years. So even be quick. 10,000 into one place. So 0.3 divide by two Jace, but 20. So this is coming out to be 13,468 $0.55 and biopsy time. Peter, this 15 years, therefore able big were to 10,000 into one plus 0.0 treat divide by two, they spot 30 so this is coming out to be 15,630 $0.8.

Ankit Gupta · Answer

question. $2500 is invested at an interest rate off 2.5% per year. Compounded daily. You have to find the values investment after the given number of years. So the formula for that this is equal to be into one plus r, divided by N holdings by anti that is the principle amount oddest of eight men specimen and is the number off times The interest is being compounded, but here is the number of years, according to the question is a Quito 2500 Sorry P is equal to 2500 artistic quinto 0.25 and is a quick 365 because injustice mean compounded daily. Now the value of tea is given to us in part A as two years. Therefore, a will be equal to 2500 into one plus 0.25 divided by 365 hold race, but she 165 into don&#x27;t. So this is coming out to be 2628.17 daughters. But T is acquired toe three years, so amount will be equal to 2500 into one place, 0.25 Divide by 365 whole race by 365 into three. So this is coming out to be 2694 point seven dollars. In part, C T is equal to six years. So is 1/4 final amount of 2500 into one plus 0.25 divided by 365 whole race by 365 and took six, so this is coming out with $2904.57.

Problem

If $\$ 3500$ is invested at an interest rate of $…

Problem 33 Easy Difficulty

If $\$ 2000$ is invested at an interest rate of $3.5 \%$ per year, compounded continuously, find the value of the investment after the given number of years.
a. 2 years
b. 4 years
c. 12 years

Answer

(a) $\$ 2145.02$
(b) $\$ 2300.55$
(c) $\$ 3043.92$

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(a) $\$ 2145.02$(b) $\$ 2300.55$(c) $\$ 3043.92$

College Algebra

Anna Marie V.

Heather Z.

Maria G.

Michael J.

Absolute Value - Example 1

Absolute Value - Example 2

James Stewart, Lothar Redlin, Saleem WatsonCollege Algebra

Anna Marie V.

Heather Z.

Maria G.

Michael J.

(a) $\$ 2145.02$
(b) $\$ 2300.55$
(c) $\$ 3043.92$

James Stewart, Lothar Redlin, Saleem Watson

College Algebra