How long will it take for an investment of $1,000 to double in value if the interest rate is 7.5% per year, compounded continuously?

Question

I'm doing test corrections for my pre-cal class and Ive got the answer (9.24 years) i just need to know how to get there because I used the wrong equation the first time (2000=1000e^7.5t). 

Answer 1

A = Pe^rt 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