How long would it take for an investment to double its value

How long would it take for an investment to double its value if it earns 6.5% per year compounded continuously? (Give your answer in years and round it to two decimals). Type in your numerical answer only; do not enter the word \"years\" or any letters.

Solution

Formula for continous compounding:

A = Pe^(rt)

where A = amount ; P = principal r = rate = 0.065 ; t = time

Time for amount to become double:

2P = Pe^(0.065t)

2 = e^(0.065t)

take natural log on both sides:

ln(2) = 0.065t

t = 10.66