Business Math
posted by Jannet on .
How long will it take a $400 investment to be worth $700 if it is continuously compounded at 12% per year?
I got the answer 6.71 years, but it was wrong, using the A=Pe^rt
Thank you

Pt = Po*e^rt.
r = 12%/100% = 0.12 = APR expressed as a decimal.
t = Time in yrs.
Pt = 400*e^0.12t = 700.
e^0.12t = 700 / 400 = 1.75.
0.12t = 0.55962.(Hit Ln key).
t = 4.66 yrs.
OR
e^0.12t = 700 / 400 = 1.75.
Take Ln of both sides:
0.12t*Ln(e) = Ln1.75.
0.12t*1.0 = 0.55962.
t = 0.55962 / 0.12 = 4.66 yrs.