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
Oct 13, 2015

Answer:

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

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 #8.5%# really means multiplying by #(100+8.5)/100 = 1.085#, we want to solve:

#600 * 1.085^t = 800#

Divide both sides by #600# to get:

#1.085^t = 4/3#

Take logs of both sides to get:

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

Divide both sides by #log(1.085)# to get:

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

Oct 13, 2015

Answer:

#t = 3.35 Years#

Explanation:

This can be solved using continuous compound interest formula

#A=pe^(rt)#

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,

#800=600.e^(0.085.t)#
#800/ 6000=e^(0.085t)#
#1.33 = e^(0.085t)#

Taking natural log(ln) on both sides
#ln(1.33) = ln(e^(0.085t))#
#0.285 = 0.085t#
#t = 3.35 Years#