How long will it take if the interest is instead compounded continuously?

Question

A very safe treasury bond has an interest rate of 2.5%. If the bonds interest is compounded monthly, how many years until a $10,000 bond doubles in size to $20,000. How long will it take if the interest is instead compounded continuously?

Answer 1

A = p(1 + r/n)^nt

20000 = 10000(1 + 0.025/12)^12t

2 = 1.0020833^12t

ln 2 = (12t)(ln 1.0020833)

0.693147 = 12(0.0020811)t

Solve for t and answer

20000 = 10000e^0.025t

2 = e^0.025t

ln 2 = 0.025t

0.693147 = 0.025t

Solve for t and answer