Find the time required for an investment of 5000 dollars to grow to 7400 dollars at an interest rate of 7.5 percent per year, compounded quarterly.
Your answer is t= years.
I got to the point where i have $74000=5093.55^{4t}$ and then I tried putting natural logs in front of both sides of the equation but from there I can't seem to cancel out what I want to to solve for t.
Best Answer
Solve $$A=P\left( 1+\frac{r}{n} \right)^{(nt)}$$ for $t$ with your values included in the formula.
Recall from properties of logarithms: $$ \begin{align*} y=x^k \Rightarrow \log y &= \log x^k \\ &=k\log x. \end{align*} $$ Hence $$k=\frac{\log y}{\log x}.$$
It looks like that exponent rule is where you are getting hung up.