Question

Priscilla invests $10,000 in an account that compounds interest continuously and earns 11%. How long will it take for her money to double? Round to the nearest tenth of a year.

Answer 1

Answer:

Step-by-step explanation:

When the interest compounds continuously, our formula is

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

If we start with 10000 and are looking for how long, t, it takes to double, we are looking for how long it will take for our account to have 2 times 10000.  That's 20000.  Therefore, our equation is

$20000=10000e^{.11t}$

Divide both sides by 10000 to get

$2=e^{.11t}$

Take the natural log of both sides to "undo" that e:

$ln(2)=ln(e^{.11t})$

Again, since ln and e undo each other what we have now is

ln(2) = .11t and

$\frac{ln(2)}{.11}=t$ so

t = 6.3 years