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
George C.
Oct 13, 2015

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

Waleed A.
Oct 13, 2015

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

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