SOLUTION: How long does it take for an investment to double in value if it is invested at 16​% compounded monthly question mark  Compounded​ continuously?

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Question 1153394: How long does it take for an investment to double in value if it is invested at 16​% compounded monthly question mark  Compounded​ continuously?
Found 3 solutions by MathLover1, MathTherapy, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Use the formula A=P%281%2Br%2Fn%29%5Ert
r=16%E2%80%8B%=0.16
n=12-compounded monthly
you want A+=+2P (double your money)
2P=P%281%2B0.16%2F12%29%5E%280.16t%29
2=%281%2B0.13333%29%5E%280.16t%29
2=%281.13333%29%5E%280.16t%29.......use log
log%282%29=log%28%281.13333%29%5E%280.16t%29%29
log%282%29=%280.16t%29log%281.13333%29
log%282%29%2F%280.16%2Alog%281.13333%29%29=t
t=log%282%29%2F%280.16%2Alog%281.13333%29%29+
t=log%282%29%2Flog%281.13333%5E0.16%29
t=34.6 years

Compounded​ continuously:
A=P%2Ae%5E%28rt%29
you want A+=+2P, and r=16%E2%80%8B%=0.16
2P=P%2Ae%5E%280.16t%29
2=e%5E%280.16t%29.....use natural log
ln%282%29=ln%28e%5E%280.16t%29%29
ln%282%29=%280.16t%29+ln%28e%29
ln%282%29=%280.16t%29+%2A1
0.16t=ln%282%29
t=ln%282%29%2F0.16
t=4.33217 years


Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!
How long does it take for an investment to double in value if it is invested at 16​% compounded monthly question mark  Compounded​ continuously?
MONTHLY:

matrix%281%2C3%2C+12t%2C+%22=%22%2C+log+%28%281+%2B+.04%2F3%29%2C+%282%29%29%29 ----- Converting to LOGARITHMIC  form

She's WRONG, AGAIN!!
The RULE of 72 ALSO demonstrates that it should be about 4.5 years!


CONTINUOUSLY:

matrix%281%2C3%2C+.16t%2C+%22=%22%2C+ln+%282%29%29 ----- Converting to LOGARITHMIC (Natural) form


There it is!!! THAT'S ALL!! 
These people are writing complex "NOVELS," and still end up with a WRONG answer. Don't they know anything about mathematics? Most likely NOT! 
How can doubling take over 34.6 years, compounded MONTHLY - according to someone who doesn't seem to have a clue - but takes 4.33 years when compounded continuously?

Answer by ikleyn(52817) About Me  (Show Source):
You can put this solution on YOUR website!
.

2A = A%2A%281%2B0.16%2F12%29%5En,


where "n" is the number of months.


Divide by A both sides


2 = %281%2B0.16%2F12%29%5En,   or, equivalently


2 = 1.013333%5En.


Take log base 10 from both sides


log(2) = n*log(1.013333)


n = log%282%29%2Flog%28%281.013333%29%29 = 52.3 months = 4 years and 5 months (rounded as required).    ANSWER