Can someone steer me in the right direction? Here's the question.

Envision that you have served as business manager of Media World for over 2 years. You have noticed that for the last 12 months the business has regularly had cash assets of $20,000 or more at the end of each month. You have found a 6-month certificate of deposit that pays 6% compounded monthly. To obtain this rate of interest, you must invest a minimum of $2,000. You have also found a high interest savings account that pays 3% compounded daily. Based on the cash position of the business at this time, assume that you decide to invest $4,000

1. Assume that you will invest the full amount in a certificate of deposit.

a. What would be the future value of the CD at the end of the investment term?

b. How much interest would the investment earn for the period?

c. What would be the effective rate of the investment?

  1. 0
  2. 1
asked by Cathy
  1. One reason I'm leery of this question is "6% compounded monthly". If that's supposed to mean 6% per month, which is what it seems to mean, it's a crazy interest rate, over 100% p.a. (3% compounded daily is even crazier! Waay crazier!)


    Anyway, in general, if you have x% interest compounded, you multiply by

    (100+x)/100 at every interval, which means that if you have y intervals, your original money is multiplied by


    6% compounded at each of 6 months would therefore multiply your original capital by


    b. Given that you know the final value, subtract your original capital, and what remains is interest.

    c. I'm not sure what they mean by "effective rate". If they mean the equivalent % p.a. the answer will be about 101.2%

    posted by jim
  2. Thanks for answering jim. So, for a. that would be $4000 + 6%. or is it 3%? diveded by 6 months? I'm really confused by this one.

    posted by Cathy
  3. It would be 4000 * 1.06^6, which is 5754.08 after six months.

    posted by jim
  4. Thanks. And for b. I subtract 4000 from
    5754.08 to get the interest?

    posted by Cathy
  5. Think of it this way:

    After 1 month, you're 6% up, which is an extra 240.

    Next month, you get 6% of 4240, which is an extra 254.40, and you throw that into the pot.

    Next month, you start with 4494.4, and throw another 6% onto that again.

    Working through an example like this month by month is boring, but the best way I know of to get to grips with the figures.

    posted by jim
  6. And for b. yes.

    posted by jim
  7. Ok thank you. How did you get the 101.2%
    for c.

    posted by Cathy
  8. (1.06^12 - 1) * 100

    posted by jim
  9. Or you could so it this way:

    Start with one dollar.

    Add 6% to it.

    Add 6% to that.

    Add 6% to that.

    and so on for 12 months.

    At the end, you have $2.01 (ignoring rounding). $1 of that was your principal, so $1.01 is interest paid during the year, which is 101%.

    posted by jim
  10. Alright, I no I'm a little slow with this,
    but can you explain the numbers
    1.06^12 - 1)*100. 1.06 is the 6% right? what is the ^12-1 and 100. Sorry to be a pain, this is the first time I'm doing this type of thing.

    posted by Cathy
  11. Look at my second explanation.
    That takes it one step at a time.

    Each month, you have 1.06 as much as you had the month before, so at the end of the 12 months you have


    as much as at the start. That is

    1.06 to the power of 12 = 1.06^12

    But you have to subtrac your original principal, which is not part of the interest.

    As I say, the best way to see it is with a calculator. Enter your principal, and keep multiplying by 1.06 for each compounding period.

    posted by jim
  12. I'll give it a shot. Thanks so much for your help, I really appreciate it.

    posted by Cathy
  13. Jim, quick question. What it I wanted to to invest the $4,000 in the high-interest savings account. Which is the savings account that pays 3% compounded daily.

    How do you multiply the daily number? multiply the 4,000*3%*365

    posted by Cathy
  14. You have to take the

    4000, and add 3% for the first day

    and then add 3% to your answer for the second day

    and then add 3% to your answer for the third day

    How do you add 3%? Multiply by 1.03.

    So just take your 4000 and multiply it by 1.03, and repeat the multiplication 365 times.

    That is NOT the same as 4,000*3%*365.

    What you want is 4000*1.03*1.03*1.03*1.03*1.03*1.03*1.03*1.03...
    and so on.

    posted by jim
  15. Thanks again, really appreciate it.

    posted by Cathy
  16. Wait, is there a way to do this on a calculator? Like 1.03*365

    posted by Cathy
  17. Right. It's not 1.03*365.

    It's 1.03 to the power of 365

    aka 1.03^365

    also written 1.03 with 365 written in superscript above and just to the right of 1.03.

    The power key isn't on all calculators.

    Scientific calculators usually have this function, and it's usually on a key marked x^y (like the Windows calculator in scientific mode) or a key with a large x and a smaller y above and to the right of it.

    The Windows calculator (use View / Scientific) gives me


    as the answer to 1.03^365, if you want to check your numbers.

    posted by jim
  18. P.S. Yes, this would mean that if you started with $4,000, at the end of the year, you would have

    $4,000 * 48482.72

    = $193,930,880

    (and you took the measly 6% per month? :-)

    posted by jim
  19. Thanks so much Jim.

    posted by Cathy
  20. What would I receive at the end of 6 months?

    posted by Cathy
  21. What value would I receive at the end of 6 months?

    posted by Cathy
  22. In case you ever come back to this, I just saw MathMate answering the same question, but reading "6% compounded monthly" as "6% _per annum_ compounded monthly".

    This makes it a whole different question, and incidentally brings the interest rates back into the land of the normal.

    posted by jim

Respond to this Question

First Name

Your Response

Similar Questions

  1. spanish help

    Hello, I need to do an essay on this question and have problem understanding the play could you steer me in the right direction in which acts to look for for this question. In Knight of Olmedo was meant to be a tragicomedy, but
  2. Oganizational Communications

    I need an example of an organizational writer that is unethical in his/her in writing. Can somone please steer me in the right direction? Thanks in advance!
  3. Physics

    A ball is thrown horizontally from a height of 16.01 m and hits the ground with a speed that is 5.0 times its initial speed. What was the initial speed? This question really boggles my brain. I have no idea how to solve this,
  4. Religion

    Hello, for On the road to Emmaus in Luke 24: how would bias possibly played a role with the follower's. can you steer me in right direction. thanks
  5. Physics

    The speed of the boat on still water is 100km/h. The water flows from the west at a speed of 45km/h. In which direction must the sailor steer the boat in order to fly due to north? *What I don't understand is 'which way(direction)
  6. Algebra

    Now this next question I unfortunately don't get at all: ~Chow Li is planting a border of 48 seedlings that will completely surround a rectangular garden plot. He wants to plant the seedlings 2 feet apart. If the garden plot is to
  7. statistics

    The weights of steers in a herd are distributed normally. The standard deviation is 200 lbs and the mean steer weight is 1200 lbs. Find the probability that the weight of a randomly selected steer is less than 1560 lbs. (Round
  8. Mass Communication Studies

    I need to find two websites. One has to be a "for profit" and one not for profit organization. Can someone please steer me in the right direction? Thanks!
  9. Psychology Life coaching

    Hello, can you steer me in the right direction of what my professor it looking for? We need to find a book and critique it on the subject of life coaching. Would any book by john c. maxwell work. thanks
  10. One for drwls

    Thank you for answering my question. Can you steer me to making a quadratic from 1/4(x+3)^2-4 Then I can get the intercepts. Thanks Just multiply it out to put it in the standard form, ax^2 + b^2 + c (1/4)(x+3)^2-4 = (1/4)(x^2 +

More Similar Questions