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%

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.

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

Thanks. And for b. I subtract 4000 from

5754.08 to get the interest?

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.

And for b. yes.

Ok thank you. How did you get the 101.2%

for c.

(1.06^12 - 1) * 100

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%.

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.