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 * e^(0.09 * t)`

`2=e^(0.09 * t)`

Taking natural log on both sides

`ln(2)=0.09 * t`

`t=(ln(2)/(0.09)`

`t=7.702`

Therefore it will take 7.702 years to double the amount