CPhill

The interest formula for continuous compounding is given by:

I = Pe^rt  Where P is the amt invested (34500), r is the rate (.066) and t is the time (30)

So we have

I = 34500e^(.066)(30) = $249874.63

Not bad, huh???

Nice try, GoldenLeaf, but I believe you gave compound interest.

The formula for simple interest is:

I = Prt   where P is what we invest, r is the rate, and t is the time in years.

So in the first case. we have

I = 5000(.085)(4) = $1700

In the second case, we have

I = 5000(.08)(4.5) = $1800 ......(54 months  = 4.5 years)

Choice 2 is better. Note that the amount we start with doesn't matter. (.085)(4) = .34,  but (.08)(4.5) = .36. So, as long as we start with the same amount, Choice 2 is always better!!

Let's think about it in groups of 20.

Note, from 1  to 20, 5 numbers are divisible by 4.....4, 8, 12, 16, 20

And since there are 5 "20s" in 100, then 5 X 5 = 25 numbers divisible by 4.

Likewise, there are 4 numbers divisible by 5.......5 , 10 , 15 , 20

And again, since there are 5 "20s" in 100, then 5 x 4 = 20 numbers divsible by 5.

However, we have to subtract out the numbers divisible by both 4 and 5 to prevent "double counting."

These would be 20, 40, 60, 80 and 100.

Thus, we have 25 + 20 - 5 = 40 numbers divisible by 4 or 5 from 1-100, inclusive.

I think you might be getting something confused, here.

The volume of a pyramid (with 3 or four sides) = (1/3) (area of the base) (height)

The surface area of one side is just (1/2 the base on that side) x ("slant height" on that side).

Thus, the surface area of all of the sides is found by totaling the surface area of all the individual sides.

If the base is an equilateral triangle, we can find the area of one side and multiply by 3. If it's a square, we can find the area of one side and multiply by 4. If it's a rectangle, we can find the area of two adjacent sides and multiply by 2.

Also, the area of the base must be considered. For a triangular base, it's just (1/2 the length of a side times an altitude drawn to that side). For a square base it's just the length of one of the sides squared. And if it's rectangular, then it's just the product of two adjacent side lengths.

I hope that helps.

(900 - 750) / 750 = 20% of the original amount free

To see this, note that they're "giving" you 150 ml "free"

This is  (1/5) of 750  = 20% "free"

Of course, my response is ....Why don't they let you pour 150ml out of the bottle and you can walk out of the store for nothing??

I guess it doesn't work that way, huh??

Of course...your mileage may vary...but here's what I've found on the web:

If I could draw a pic, I would.....

Now, the radius of the Earth must be 3960 miles...

And converting 200 ft to miles we have 200/5280 ≈ .0378 miles

Note that the line of sight is tangent to the Earth's radius where they intersect.

So, we have a right triangle with a hypoteneuse of  3960 + .0378 = 3960.0378 miles

And one leg is the Earth's radius. So by the Pythagorean Theorem we have

√(3960.0378²  - 3960² )  ≈ 17.3 miles

OK...so we have

1000(1 + r)(1 +r) = 1210      divide by 1000

(1 + r)²    = 1.21      take the square root of both sides

1 + r = 1.1               subtract 1 from both sides

r = .1  = .10 = 10%

How's that??

Thanks...alan....I've answered so many questions that I'm going snowblind!!!

It is worth $1210 now    the interest earned is $210

Simple interest

I = Prt

210 = 1000(r)2

210 = 2000 (r)

r = .105 = 10.5% = simple interest rate

Compound Interest

1210 = 1000(1+ r)²    Divide both sides by 1000

1.21 = (1 + r)²           Take the log of both sides

log 1.21 = log (1 + r)²    By a property of logs, we have

log 1.21 = 2 log (1 + r)    divide by 2 on each side

(log 1.21) / 2 = log (1 + r)

.041392685158225 = log (1 + r)

So we have

10^{.041392685158225}  = r + 1

1.099999999999999897 = r + 1   subtract 1 from both sides

r = .0999999 =  9.99999% = 10% = compound interest rate