if-3000-is-invested-at-5-interest-find-the-value-of-the-investment-at-the-end-of-5-years-if-the-inte

Question

If $\$ 3000$ is invested at 5$\%$ interest, find the value of
the investment at the end of 5 years if the interest is
compounded
(a) annually
(b) semiannually
(c) monthly
(d) weekly
(e) daily
(f) continuously

Caleb Miller · Accepted Answer

Hey, guys, welcome back. We&#x27;re told that we have initial investment of $3000 at 5% interest. We were asked to figure out how much said investment will grow at different interest annual interest. Semiannual monthly, weekly daily. Continuously. We&#x27;ll use our equation. Our amount after sometime is able to our initial amount our initial amount being the 3000 plus our rate over end over end to the team and r T. It&#x27;s how many years. So in this case, he would be five for all these things two years ago to five. And then end is how many times per year times per year. So first we were asked to figure out what happens. It&#x27;s calm, pounded annually, so his compound annually than end is simply one part a and his one I have 3000 one plus r ever end are is 0.5 Number one raised to the end T and we said was one t value is five. And if you do the math, that comes out to 3000 828 0.84 Next problem. Rest figure. What happens if this compound id semi annually? So for semi annually than end will be equal to two. I will say that a city should have said That appears well. A city is equal to 3000 one plus 10.5 and is not to times that by to to the five. And that will give us a value of 3000 140 0.25 Next, we&#x27;re asked to figure out what happens if it&#x27;s calm. Pounded monthly 12 months and years and his 12 and we have a He is evil Toe 3000 one plus 10.0 5/12 0 5/12 I replied by two times 12 and that comes out to 3000 850 0.0 eight. Next to ask to figure out what happens if it&#x27;s compound ID weekly in its weekly. There are 52 weeks in a year, so our equation becomes. Eight of the tea is equal to 3000 3000 one plus 10.5 over 52 multiplied by 52. I&#x27;m sorry. I apologize up here. I had a slight mistake. Our experts should have been 12 multiplied by five and this answer is still correct. That was the correct answer. Going back now. Down to Part D. You do this math? Get a value of 3000 851 0.61 now for part, you were asked for your what happened to his compound it daily. There are 365 days in a year. To me, it&#x27;s not only beer, we&#x27;ll have a Sebti people of 3000 one plus 0.5 3 65 raised to the five years times 365 times every year. If you do the math on that one, that comes out to 3000 800 3000 800 52 $01. Part of the rest of you know what happens. It&#x27;s compound to continuously. Basically, we&#x27;re saying what happens when N goes to infinity or any ghost Infinity, Our equation turns into a city is ableto our initial value. Times e. Raised to the rt becomes 3000 times E Raised to the are just 0.5 times T just five, and that comes out to three 1000 800 to point a sense. Now it&#x27;s part F that includes parts A through F, and that includes the problem. Thanks for watching

Amy Jiang · Answer

Okay, so for this question, we were asked to find and just earned, which is a calling a $10,000 investment. So that means our r p medical to 10,000 and are it&#x27;s invested for five years. So that means our your which is T is equal to five. And our Bates is 4%. That&#x27;s our is equal to 0.4 on our M. That&#x27;s are sometimes for a year for tears. So for partying, we have, um, annually. So that&#x27;s just once a year. So that means we have our equation. A is equal to P times one plus or over em. That is one to the power of T, which is five times one and now for somewhere annually. That&#x27;s equal to twice a year. So that&#x27;s division or R M value is not, too, And then we have quarterly. That&#x27;s four times so far, is not four, and then we have month me. That is every month, and there&#x27;s 12 months in the year, so that&#x27;s 12. And then for continuously, we have a different formula that is, we have a is equal to P, which is 10 doesn&#x27;t kinds E. R. which is 0.4 times to you, which is fine. And I forgot that to rewrite my P. That&#x27;s 10,000. So let me just put it is equal to 10,000 for each one. You know, you could just put that into a calculator to solve your events were to get the, um, answer.

Lourence Gonhovi · Answer

all right, so 10,000 is invested for 10 years it uninterested or 5% off a different compounding periods. So we&#x27;re going to follow through all the compounding periods, starting with compounded annually, which is our a a sp animals. So the animal is equals True 10,004 p, then one plus, uh, one last little 10.5 which gives us 1.5 and then to the power 10. Then when we work this one out to get 10,000 288 0.95 around the Gulf and then be part we want to compound in Dakota. So the quarter the interest rate is going to be divided by four and the compounding the period, and we also multiplied by four. So a P is 10,000 one class 0.5, led by four at 100 plus one is 1.125 125 That&#x27;s compounded per quarter And how many quarters are in 10 years there, 40 quarters and then these are blocks made to 16,000 436 0.20 All these are in dollars and then our C we are going to compound per month. So is it cost to 10,000? 10,000? More than 1000. Then we&#x27;ll say we have caught five, they said, divided by 12 plus one. Then we get one point 00 for one and then six, carrying all to the power 120. And then we&#x27;ll get approximately 16 for 70 0.9 and it&#x27;s in dollars. And from there we work out our D Our d is daily so daily it will be a is equals to 10,000 and then they need to be 5% divided by three handled and all right. 65. There were year You&#x27;ve got trouble 65. Yeah, And then we add, you know, one day and we&#x27;ll have a red off one point. It was 00 136 1986. And this would be to the power off, um, 10 times 365 And that will be three 50 like zero. And but to give us the value off $16,000. 486 0.65 Lastly, we want to use the continuous right, So the convenience straight is a Z goes to present value applied by mhm eating to the power off I t. And this would be equal to 10,000 b to the power off I is That&#x27;ll point in this little fight terms T which is the period off 10 years and then this would give us 16 487 point to one and does it?

Julian Wong · Answer

problem. We want to come up with a formula for Thea amount of investment based on the different compounding period. So let&#x27;s set up the general form first. The future value is equal to a present value of $10,000. Ah one plus the rate is 11% over 100 k k being the compa number of compounding periods in a year for a period of five years. So it will be to the power of five K. Um, so, in a, B, C and D, they just correspond to a specific value for Kay. So, for example, annually, that just means once a year. So that will be one plus 11 over 100 times one which is just 100 to the power of five times one, which is just five. And ah, we use a calculator do this. So one, ah 0.11 to the power of five and then times 10,000 that will give us a ah future value of $16,850.58 in part B. The ah que value here is going to be 12 because its monthly so 100 times 12 on the denominator and five times 12 and the exponents. So putting that into a calculator spun to the power of 60 and then times 10,000 that&#x27;ll give us a future value off $17,289.16. Part see daily, that&#x27;s 10,001 plus 11 over 100. There are 365 days in a year. So K is gonna be 3 65 Putting that into a calculator, make sure you follow the order of operations that will give us a future value of 17,331 and nine cents. And lastly hourly. We need to calculate how many hours there are in a year. So, uh, one year ah is ahh, 365 days and one day as a 24 hours. So this will be our conversion. That will give us 8760 hours, which means our future value year for Part four party is 10,000 times one plus 11 over 100 times 1000 760 to the power of five times 8760 again in a calculator that will give us ah future value of $17,332 and 47 cents

Amy Jiang · Answer

Okay, So for this question, we&#x27;re asked to find our interest rate that is acquired foreign investment off 5000. That means our investment, which is P NZ 5000. And we wanted to grow to 7500. That means are a is 7500. And we know that our years that&#x27;s tea in pickle chip five years. If the interest is compounded, that follows. So for part A, we have annually, so that means our value is equal to one. So we&#x27;re asked to find our rates. So let&#x27;s plug that in. So we have 7500 is equal to 5000 times one plus on, which is, um, what we&#x27;re solving for over em. That&#x27;s one all day tomorrow, five times one. And now it&#x27;s solved for corn, so are divided by 5000 1st we have 7500 divided by time, though that that&#x27;s equal to one plus or to the power of five. And no, um, well, multiply both science by 1/5 to get rid of our power. So now we have fallen is equal to one plus car and subtracting one from both sides. You should get or okay, and I&#x27;ll upload this intimate tactically to dissolve for our okay. It&#x27;s assumed that apart from your divided by 5000 to power of 1/5 and when it&#x27;s won, that&#x27;s equal to an interest. Rates off 0.84 and now for part B, we woods quarterly. So that&#x27;s when, um, RM value equal to four. So since we&#x27;re paying four times every year, comes in a copy and paste this and change RM value observant one piece I like some. Okay, so changed our 1 to 4 and I was gonna do the same thing. We&#x27;re going to solve a four or five times for that&#x27;s 20. Now it&#x27;s alive by 5000. Now let&#x27;s take both sides to tow 1/20 power to get rid of a bar power on our right inside. So we get the falling. You get 7500 over 5000 to the part of 1/20 minus one that&#x27;s equal to our, which is equal to let&#x27;s see 7500 divided by 5000 to the power of 1/20 minus one that&#x27;s equal to 0.20 which is equal to 20% That&#x27;s going on. And then this one is, um no, Sorry. That&#x27;s not 20%. We&#x27;re gonna move to that Something places. So that&#x27;s 2%. And this is eats point for presents.

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.

Problem

(a) How long will it take an investment to double…

Problem 19 Medium Difficulty

If $\$ 3000$ is invested at 5$\%$ interest, find the value of
the investment at the end of 5 years if the interest is
compounded
(a) annually
(b) semiannually
(c) monthly
(d) weekly
(e) daily
(f) continuously

Answer

a) $$
\$ 3828.84
$$$$
\$ 3840.25
$$
b) $$
\$ 3840.25
$$
c) $$
\$ 3850.08
$$
d) $$
\$ 3851.61
$$
e) $$
\$ 3852.01
$$
f) $$
\$ 3852.08
$$

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Video Transcript

James Stewart

Essential Calculus Early Transcendentals

Grace H.

Catherine R.

Kayleah T.

Michael J.

Precalculus Review - Intro

Functions on the Real Line - Overview

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a) $$\$ 3828.84$$$$\$ 3840.25$$b) $$\$ 3840.25$$c) $$\$ 3850.08$$d) $$\$ 3851.61$$e) $$\$ 3852.01$$f) $$\$ 3852.08$$

Essential Calculus Early Transcendentals

Grace H.

Catherine R.

Kayleah T.

Michael J.

Precalculus Review - Intro

Functions on the Real Line - Overview

James StewartEssential Calculus Early Transcendentals

Grace H.

Catherine R.

Kayleah T.

Michael J.

a) $$
\$ 3828.84
$$$$
\$ 3840.25
$$
b) $$
\$ 3840.25
$$
c) $$
\$ 3850.08
$$
d) $$
\$ 3851.61
$$
e) $$
\$ 3852.01
$$
f) $$
\$ 3852.08
$$

James Stewart

Essential Calculus Early Transcendentals