Compound Interest: Solving for an unknown variable for time

Problem 25 Section 4.5: How long will it take a $5000 deposit to double, if invested at a 9.25% rate and compounded Daily.

Recall: The formula for compound interest is A= P(1+ (r/n))^(n*t)
Notice, it does not state outright what the A is going to be. But it does tell you that they want the deposit to double, that deposit it p=$5000. Thus A must be equal to $10,000. Since they tell us that the interest is compounded daily, we know that n=365. Converting the rate of interest into a decimal, 9.25% = .0925

Given the information above, we can set up our equation and solve for the unknown t

10000=5000(1+(.0925/365))^(365*t)
2=(1+(.0925/365))^(365*t)
ln 2 = ln (1+(.0925/365))^(365*t)
ln2= 365*t*ln (1+(.0925/365))
ln2/ [365*ln (1+(.0925/365))]=t

Audio File: Calculator Approximation Problem 25 Section 4.5