Question

How long will it take for the balance of an account to double if the savings account earns 0.75% annual interest compounded monthly?
Hint: Set up the problem using the formula: A=P(1+r/n )^nt.

Answer 1

You're looking for the time $t$ that it takes for the principal $P$ to double, so $A=2P$. Dividing both sides of the formula by $P$ leaves you with

$2=\left(1+\dfrac rn\right)^{nt}$

You're given that the account earns 0.75% interest and that the interest is compounded monthly, so $r=0.0075$ and $n=12$.

$2=\left(1+\dfrac{0.0075}{12}\right)^{12t}$
$\ln2=\ln\left(1+\dfrac{0.0075}{12}\right)^{12t}$
$\ln2=12t\ln\left(1+\dfrac{0.0075}{12}\right)$
$t=\dfrac{\ln2}{12\ln\left(1+\dfrac{0.0075}{12}\right)}\approx92.45$