Search 74,321 tutors
FIND TUTORS
Ask a question
0 0

how long will it take for 490 to grow to 1093.34 at 5 percent

I really need help solving this problem im stuck and I cant find a way out of it Im trying to find a way to solve it or for someone to show me how to solve it

Comments

In order to solve this problem you have to specify the time interval the 5% applies to. Is it 5%/day 5%/week or 5%/year.
 
The general solution is T= (Ln(1093.4/490))/.05 =62.1 but since the time interval has not been specified we can not say that it is 62.1 sec, min, hours or years so the question as stated can not be answered.
Jim
Tutors, please sign in to answer this question.

1 Answer

Hi, I have worked out your problem.  You have to solve for t given an equation and 3 of the five unknowns.
first let's just solve the general equation for t. This is the general equation;
P=C * ( 1 + r/n ) ^ ( n * t )
divide by C
P/C = (1+r/n)^(n*t)
take the log of both sides so that t is in the base
log(P/C) =log(1+r/n) * n * t
divide bye the log stuff and n
log(P/C)/(n*log(1+r/n)) = t
 
Next the solving part. 
We don't know n so we can simplify the equation for n = 1, and n = infinity.
n = 1 then the above equation becomes;
t = log(P/C) / (1*log(1+r/1)
t = log(P/C) / log(1+r)
lets substitute in now. 
t = log (1093.34/490) / log(1.05) ....... your equation you forgot to add one to the denominator.
t = 16.45 years ====> this equation's units are in years.  You can see that if you know that n is defined as the number of times per year it is compounded.
 
Part two, we don't know n so let it approach infinity ... n can't ever get there , so in math we take a limit to find what values of things are where infinity is involved
 
if you take the limit as n approaches infinity of the general equation you will get;
t  = log (P / C) / r
so then t = log (1093.34/490) / 0.05
t = 16.05 years
the two answers you should submit are then,
t = 16.45 years with n = once / year
t = 16.05 years with n = infinite times / year
 
If you don't know what limits are and don't know where I came up with any equation let me know, and I will try to explain it to you.  I don't know what kind of class you're in, so I don't know what level of knowledge you have.

Seattle Math tutors