# If $600 is deposited in an account paying 8.5% annual interest, compounded continuously, how long will it take for the account to increase to $800?

##### 2 Answers

#### Explanation:

This answer reflects my understanding of compound interest. It may be that the correct rate for continuously compounded interest results in a higher effective annual interest rate.

Since adding

#600 * 1.085^t = 800#

Divide both sides by

#1.085^t = 4/3#

Take logs of both sides to get:

#t log(1.085) = log(4/3)#

Divide both sides by

#t = log(4/3)/log(1.085) ~~ 3.52638# years#~~ 1288# days

#### Explanation:

This can be solved using continuous compound interest formula

p = principle interest

r = annual interest

t = number of years

A = Amount after n years including interest

Here,

p = 600

r = 8.5 / 100 = 0.085

t = 800

so,

Taking natural log(ln) on both sides