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?
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!)
a.
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
((100+x)/100)^y
6% compounded at each of 6 months would therefore multiply your original capital by
1.06^6
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%
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.
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
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
48482.724527501361858081469898097
as the answer to 1.03^365, if you want to check your numbers.
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.
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