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
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.