maths

I'm assuming that, if you want your money to "quadruple," you want to end up with $32000 - 4 times what you started with,. Thus, you want to earn $24,000 of interest PLUS your original $8000.

The "formula" for the interest computation is I = Pe^(rt), where P is the amount we started with ($8000), e is the base of the natural log (i,e., about 2.718), r is the interest rate expressed as a decimal (i.e., .045), and "t" is what we want to find!! (Note that the "rt" is an exponent on e!!)

So, let's get started!!

We have, 24000 = 8000* e^ (.045t)

Divide both sides by 8000 and we get

3 = e ^(.045t)

Now, take the LN (natural log) of both sides. We have

LN 3 = LN e^ (.045t)

Note, that by the property of logs, the right side just becomes .045t. (That's the beauty of using the LN here - it simplifies things!!)

So we have

LN 3 = .045t

Divide both sides by .045 to get "t"

(LN 3) / (.045) = = about 24.41 years!!

Note...if by "quadruple," you meant that you wanted to EARN $32000 in interest, just replace the "24000" in the equation with "32000" and follow the same process. (It should take longer than 24.41 years if you do everything correctly!!)

Hope this answers your question!!

Whoops!!

Disregard my previous answer....I didn't note that the compounding was annually rather than what I gave you which was continuous compounding!!

Well.... no biggie!!

Here's the "formula" we need

I -= A ( 1 + r/n)^(n*t)

Where .I is the interest we wish to earn (I.m assuming that you want to make $24000 to "quadruple" your money), A is what we started with, 8000 (the principal), r is the interest rate expressed as a decimal (.045) , n is the number of compoundings per period (in this case, 1 time per year) and t is, again, the time - what we're trying to find.

So we have

24000 = 8000(1 + .045)^(t) (Note that since n = 1 , we can ignore it.)

Again, divide both sides by 8000 and we get

3 = (1.045)^(t)

Now, take the LOG of both sides

LOG 3 = LOG (1.045) ^(t)

By the property of logs, we can bring the "t" on the right side "out front" and we have

LOG 3 = (t)* LOG(1.045)

Now, divide both sides by LOG (1.045) and we have

LOG(3) / LOG (1.045) = t = about 24.96 years!! (Note that the time isn't much longer than under continuous compounding!!)

Again, if by "quadruple," you mean that you want to EARN $32000, just replace the "24000" in the above equation with "32000,"...... wash, rinse and repeat!!

Sorry for my previous s***w-up. I hope this helps!!