Hello and HELP!!! U Mathematical GURUS!...
 

My niece needs to know how to solve this problem for a test.
Your help would be deeply appreciated!

Problem
u have saved $7000.00 toward the purchase of a new car costing 9000.00.
How long will the 7000.00 have to be invested at 9% compounded monthly to grow to 9000.00?

Forumlas,explanation of variables,etc... ,please.
Thanks
HappyPokering, [img]/images/graemlins/smile.gif[/img]
SittingBull

Re: Hello and HELP!!! U Mathematical GURUS!...
 

This is not really hard, did you try it yourself?

$(t): amount of dollars after t months, $(0)=7000
g: growrate, (100%+9%)/100% = 1.09

Now $(t)=$(0)*g^t, the standard exponential growth formula.
We want to know when we can buy the car, or: $(t)=9000

9000 = 7000 * 1.09 ^ t
{ division by 7000 }
9/7 = 1.09 ^ t
{ e^log(x) = x }
9/7 = ( e ^ log(1.09) ) ^ t
{ ( x ^ y ) ^ z = x ^ zy }
9/7 = e ^ t*log(1.09)
{ log, log(e ^ x) = x }
log(9/7) = t*log(1.09)
{ division by log(1.09) }
log(9/7) / log(1.09) = t

Hence, t = 2.916...

The rent is compounded monthly, so after 3 months we can buy the car.
We even have about $65 left!

I hope now you can explain it to her.

Next Time

Re: Hello and HELP!!! U Mathematical GURUS!...
 

The 9% is most likely per year, not per month.

NO,Bruce! It\'s compounded monthly at 9% n/m
 

Re: Hello and HELP!!! U Mathematical GURUS!...
 

9% monthly eh? 281% annually?! [img]/images/graemlins/smile.gif[/img]
Sign me up please.

How often it\'s compounded has nothing to do with it
 

It can be compounded quarterly, monthly, daily, hourly, or instantaneously, and the interest rate can still be given as yearly. Interest rates are almost always quoted per year unless otherwise noted. Where are you going to get 9% monthly interest? It's probably 9% per year compounded monthly. Make sure.

THANKS VERY much .wells...
 

I appreciate your complete explanation of this proble.
I dont want to aggravate u about problems that are trivial TO U. However,I'm asking your permission to consult U on future problems of this nature.
I do understand if u prefer NOT to be consulted about these types of problems in the future. I WILL honor your request. And I will let my nephew know that u gave me these solutions. They were NOT my solutions.
SittingBull
PS I'll convey the solution to my niece. She is having a test Monday. Hence,it's sort of a cram job.
My nephew,my niece's uncle, consulted me today about the problems today.
Thanks again
SittingBull

Re: How often it\'s compounded has nothing to do with it
 

Instantly? 'e'-gads.

cheap math joke...sorry [img]/images/graemlins/wink.gif[/img]

U are absolutely correct,Bruce! SORRY!..
 

I want to thank U for your i/p into my great-niece's prob.
SittingBull

Sorry,Angel! My MISTAKE! Bruce was CORRECT! n/m