Question

How long does it take for a deposit of $900 to double at 9%?

Answer 1

Solution: We know that formula for continuously compound interest is:

$A= P e^{rt}$

Where A is the future amount $900 x 2 = $1800

P is the principal investment $900

e is the eular's constant

r is rate of interest 0.09

t is the time ( to be found)

Therefore we have:

$1800=900 \times e^{0.09 \times t}$

$2=e^{0.09 \times t}$

Taking natural log on both sides

$ln(2)=0.09 \times t$

$t=\frac{ln(2}{0.09}$

$t=7.702$

Therefore it will take 7.702 years to double the amount