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