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0%6. Suppose you deposit $S00 in an accouat prying the balance _8er Syexsinterest compounded continuously; Use- = Patt to find()7.SAVINCS JVnAI account deposit of ...

Question

0%6. Suppose you deposit $S00 in an accouat prying the balance _8er Syexsinterest compounded continuously; Use- = Patt to find()7.SAVINCS JVnAI account deposit of S300 u to eu 5.8% interut Aie bowv Worth 5900? Useyea (1 +r)f ind round to the nexrest tenthEA] Wall tbt inveltmient ba

0%6. Suppose you deposit $S00 in an accouat prying the balance _8er Syexs interest compounded continuously; Use- = Patt to find ()7.SAVINCS JVnAI account deposit of S300 u to eu 5.8% interut Aie bowv Worth 5900? Useyea (1 +r)f ind round to the nexrest tenth EA] Wall tbt inveltmient ba



Answers

An investor deposits $10,000$dollar in an account that earns $3.5 \%$ interest compounded monthly. The balance in the account after $n$ months is given by $$A_{n}=10,000\left(1+\frac{0.035}{12}\right)^{n}, \quad n=1,2,3, . . .$$ (a) Write the first eight terms of the sequence. (b) Find the balance in the account after 5 years by computing the 60 th term of the sequence. (c) Is the balance after 10 years twice the balance after 5 years? Explain.

It is given that $100 is invested a great off 600 won by 2% This for a period of 10 years on it. The interest is compounded continuously. We have to calculate the final balance. So we know that if interesting scar calculated, compounded continuously, then we can find the final amount using the formula equal to P e raise too Party. Where is the natural logarithms piece? The principal amount are expressed as the rate of interest expressed us. The smell. It's just as decimal. Then t is the, uh, number of years. So here we can find find it among us equal to peace. 100 Exponential artist 6.5 expressing in the similar it will become zero point things. Five 0.65 So it is 20.65 in the dead, and this is equal to 191 point five site. This is our final answer annual amount, final amount

Have already been given the formula for in trust after end months. So I n is 100 into 1.5 to depart and minus one upon 0.5 minus. And no first part us says to calculate the for six terms of the sequence. So a sorry's I one would be equal to zero when Enezi will do one I to putting an is equal to two will get 100 in 20.5 which is 0.5 for n is equal due to no I he is 100 in 20.15 bridges or witches 1.5 So energy will do today. Hi, four is 100 in do Zito Boyne 03 That will be three for n is equal to four No, I Fife is 100 into 0.5 which is five for n is equal to five and I six is 100 in 20.75 which would be equal to 7.5 for any is equal to six No coming to part B. Sorry. No coming to part B for part B and would be equal to sensitise five fears and the interest is compounded monthly. So five into 12 which is equal to 60 months So N is equal to 60. So I and I 60 is equal to 100 into 1.5 departs 60 minus one upon 0.5 minus 60. So we'll get 100 in do 9.77 which is 9 77 So in trust after five years would be dollar 9 77

For this question who were told to use the results in Exercise 85 to find eight. So let's first write down the result from 85. So Exercise 85 tells us the accumulated value A is equal to well times one plus R over 12 to the power of 12 p minus one times one plus problem for us. So now we just need to identify what all those variables are. So for this particular question, uh, investor, there's depositing $100 on the first day of each month. So therefore, that's R P principle, so it's equal to $100. Now the account pays an annual interest rate of 2% compounded monthly, So our is 2%. So don't forget to write that and decimal format was 0.2 okay. And the last thing that we need to know is what T is or more like, what 12 t is right. So we're told that the balance in the account for five years is, um, 100 times one plus 0.2 of the 12 1 all the way up to 60 right, So the last power is 60 so Therefore, 12 T is equal to 60 which makes sense because they're a total of 16 30 60 com pounding period, since we're doing this for five years and each year has 12 months. So now we have everything we need to find a so A is going to be equal to 100 times. This will be one plus 0.0 2/12 power, 60 minus one times one plus 12 over zero point direction. So now you just have to punch this into a calculator. So let's see. That's going to be one plus to the power of 60. Subtract one and then multiplied by one plus 12 over 0.2 and you end up with a total, UH, $6315. Andi 24 cents.

So for this problem, we are given a lot of information about deposits being made into an account with a 6% interest rate. And we want to find the balance at the end of five years. Also, all the information we were given in the beginning of the problem is pretty much irrelevant because of the fact that we're already given this equation to calculate or the balance in the account. And all I have to do is sold for a So since we know that this is going to be a geometric Siri's lessons as a fixed interest rate that tells us that we're just going to be finding the sum of all the terms in this series, I'm so first off we can see that they were going to be 60 terms in this series because of the fact that we have up through to the 60th power right here. Next, we're going to you want to pull out our first room. So our first room is just going to be this whole set right here. Um, the trickiest part of this problem is noticing that this one plus 10.6 over 12 is part of our first term, and it looks like it's going to be whatever our rate is our which it actually is. But we have to make sure that we include it as part of our first term. I'm so that being said is going to be 100 times one plus 0.6 over 12. And finally our rate art. Is this a justice internal portion without the 100? So that's one plus 0.6 over 12. Um, in our book, give us a formula for finding the sum of n terms in a finite geometric sequence. Um and so this is going to be our first room A one times one minus R to the n power are common ratio raised to the power of the number of terms divided by one minus R. So only plaguing our information from this problem we find that are some which is going to correspond to our large or capital. A is equal to a one, which we know is 100 times of one plus 0.6 over 12 only in times in brackets one minus, our rate which again one plus 0.6 over 12 raised to the 60th power divided by one minus. All right of one plus 0.6 over 12. And now that we've set up this really large expression, all we need to do is simplify it. And once we do that, we find that a oh, our balance in the account is going to be approximately 7000 and $11 in 89 cents.


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