Question

how long will it take, to the nearest hundredth of a year, for an investment to triple if it is going to be invested at a rate of 11% compounded continuously

Answer 1

Answer:

Step-by-step explanation:

The formula for continuous compounding is

$A(t)=Pe^{rt}$

where A(t) is the amount after all the compounding is done, r is the interest rate in decimal form, P is the initial investment, and t is the time in years.  

If we are investing some money and want to find out how long it will take the investment to triple, let's say our initial investment, P, is 1000 and the tripled amount would then be 3000.  So we have everything we need to solve for t:

$3000=1000e^{.11t}$

Begin by dividing both sides by 1000 to get

$3=e^{.11t}$

The only way to get that t out of its current exponential position is to take the natural log of both sides and follow the rules for logs:

$ln(3)=ln(e^{.11t})$

The power rule for natural logs is to bring down the exponent out front:

$ln(3)=.11t*ln(e)$

And you should be aware of the fact that a natural log "undoes" e since they are inverses.  So what we are left with is

ln(3) = .11t

Divide both sides by .11 to get

t = 9.99 years