CPhill

Growth and Decay: Find the final value of $2500 invested at an interest rate of 2% compound monthly for 10 years.

A = 2500(1 + .02/12)^(10*12)

Where

A = The accumulated amount after some period - in this case, 10 years

2500 = the orginal principal

.02  = the interest rate expressed as a decimal

12 = the compoundings per year

10 = the number of years

Evaluating this, we have about $3053 after 10 years.

Re: what number is for hourly compound interest

I'm not aware that interest is usually compounded per hour, but we might "devise" a formula to do so.

The normal "formula" is just this

Where

A(t)  = the total amount accumulated after some period at some rate of interest

A₀ = the orginal investment or principal

r = annual rate of interest (expressed as a decimal ....   5% = .05, for example)

n = number of compoundings per year

t = time (in years)

The number of compoundings per year = 24 hours in a day x 365 days = 8760... (Note that your mileage may vary here if we have to account for a "leap" year !!!)

To find out how much interest is earned over some time period, just subtract A₀  from A(t) at the end of the period.

It might seem that hourly compounding would generate WAY more interest in a year than some other method, say, quarterly compounding, but it isn't so. For instance, 5% interest on $1000 compunded hourly for one year results in only about 33 cents more interest than the same amount at the same interest rate compounded quarterly.

Hope that helps

P.S. - There may be other forum members who are are far better versed in finance than I am. Perhaps some of them might contribute some other "formula" - if they know of one !!!

evaluate the function y=4x-7

There's nothiing to "evaluate." We would need to know an "x" value in order to be able to "evaluate" the function.

If you're using the on-site calculator, hit the "log" button on the calculator, type in the number you want to take the log of,  hit  the "=" button

24 inches divided by 12, divided by 5,280 multiplied by 49 divided by 60

Just enter it into the calculator like this

24 ÷ 12 ÷ 5280 × 49 ÷ 60

Your answer will be in inches

Re: -12/3/4

I assume you mean this:       (-12)/(3/4)

First, write the whole number as a fraction = (-12/1)

Now, invert (flip over) the second fraction = (4/3)

Now...just multiply the first thing by the second.......this gives

(-12/1) * (4/3) = (-48/3) = (-16/1) = -16

And that's it............

2(x³y⁵)²  

Remember that we have a rule of powers (exponents) that says (a^m)ⁿ = a^(m*n)

In effect, we're multiplying the "inside" power by the "outside" power

So we really have      2[ (x³)² * (y⁵)² ] = 2[x⁶ * y¹⁰] = 2x⁶y¹⁰

If 2x+3=90, then does 2x+4=100  (???)

Here's one quick way to solve this -  this "method" won't always work, but it does in this case.

Subtract 3 from both sides in the first equation and 4 from both sides in the second.

Then, in the first equation 2x = 87

But, in the second equation, 2x = 96

And since "2x" has to be the same thing in each case, then it's impossible for it to equal both 87 and 96 at the same time!!! So the second equation isn't valid, given the first!!

We're "cheating" a little bit here, but what the heck??..... I'm lazy!!!  

2/1/5 as a fraction

I assume you mean this:       (2)/(1/5)

First, write the whole number as a fraction = (2/1)

Now, invert (flip over) the second fraction = (5/1)

Now...just multiply the first thing by the second.......this gives

(2/1) * (5/1) = (10/1) = 10

And that's it............

ln e to the 5th power

I assume you mean this:    lne⁵

Note, by a property of logarithms, we have

ln(a)^b  = b*ln(a)      In other words, I can just bring the exponent (power) "out front" and multiply it by the "log" part (or, "ln" part - in this case)

So we have

lne⁵      =     5*lne

"lne" is just "1"    (It denotes the exponent that I need to put on "e" to give me "e")

So we have

5* (1) = 5

And that's all there is to it........