Compound interest on investment?

E

Enlong

New member
How long will it take an investment to quadruple in an an account that earns 5% interest rate compounded continuously?
 
M

MagicMatt

New member
The formula for continuously compounded interest is

A = Pe^(rt)

where:

A = final amount, after 't' years
P = principal (starting) amount
r = interest rate
t = time, in years

So plug in some numbers. Let's say you start with $1,000, and you want to quadruple that into $4,000.

4000 = 1000e^(0.05t)

Now solve for t:

4 = e^(0.05t)
ln(4) = ln(e^(0.05t))
ln(4) = 0.05t
ln(4)/0.05 = t
27.725 = t

So, it would take almost 27 years and 9 months.
 
V

Victor

Member
The future value of an initial principal amount compounded continuously is given by this:

FV = P(e^rt) where e is the exponential constant 2.718... etc, r is the rate of growth and t is the number of periods.

In this case, we want FV = 4P

So we are looking for 4P = P(e^0.05t) since the interest rate is 5 per cent.

So e^0.05t = 4 by dividing both sides by P

So 0.05t = ln(4) using natural logs

So t = ln(4)/0.05 = 1.3863/0.05 = 27.726 periods.

OK?
 
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