How long does it take an investment to double at an annual interest rate of 7.5% compounded continuously?

A = Pert is formula for continuously compounded interest

A = final amount = 2000

P = principal = 1000

e = euler's number (on calculator)

r = interest rate as decimal = .075

t = time in years

Your mistake is that 7.5% as a decimal is 7.5/100 = .075

not 7.5

2000 = 1000e.075t

e.075t = 2000/1000

e.075t = 2

take natural log of both sides

ln e.075t = ln 2

.075t = ln 2

t = ln2/.075

t = 9.24 years

Explanation:

Hope this helps