Question

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?

Answer 1

`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

Answer 2

`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`