How long does it take for an investment to double in value if it is invested at 4 compounded monthly

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How many years does it take for an investment to double in value if it is invested at 6%
if interest is compounded quarterly?
if interest is compounded continuously?
**
compound interest formula: A=P(1+r)^t, P=initial investment, r=interest rate per period, t=number of periods, A=amount after t periods.
For continuous compounding: A=Pe^rt
..
Quarterly compounding: A/P=2, r=.06/4=.015, t=quarters
A=P(1+r)^t
A/P=(1+.06/4)^t
A/P=(1+.015)^t
2=(1.015)^t
take log of both sides
log(2)=t*log(1.015)
t=log(2)/log(1.015)
t≈46.55 qtrs≈11.64 years
..
Continuous compounding: A/P=2, r=.06, t=years
A=Pe^rt
A/P=e^rt
2=e^rt
2=e^.06t
take log of both sides
ln2=.06t*lne
lne=1
.06t=ln2
t=ln2/.06
t≈11.55 years

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Found 3 solutions by MathLover1, MathTherapy, ikleyn:

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Answer by MathLover1(19673)

 

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Use the formula

%=
-compounded monthly
you want (double your money)


.......use log





years

Compounded​ continuously:

you want , and %=

.....use natural log





years

Answer by MathTherapy(10144)

 

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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:

 ----- Converting to LOGARITHMIC  form

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


CONTINUOUSLY:

 ----- 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(45969)

 

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.

2A = ,


where "n" is the number of months.


Divide by A both sides


2 = ,   or, equivalently


2 = .


Take log base 10 from both sides


log(2) = n*log(1.013333)


n =  = 52.3 months = 4 years and 5 months (rounded as required).    ANSWER

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