00:01
To determine how much here, you have to consider the final amount, the initial principal amount times one plus the rate as a decimal over the number of times compounded a year, raised to the power of the number of times compounded times the time in years.
00:24
So if the initial investment was $2 ,000, that's p, earned an interest of 12%.
00:32
Compounded monthly that'd be 0 .12 divided by 12 because there are 12 months in a year raises 12 times t which we're going to solve for we want to know how long is it going to take to reach $50 ,000 so to solve for t first step should be to divide both sides by 2 ,000 so 50 ,000 divided by 2 ,000 is 25 so 25 would equal and you can add 1 plus 0 .12 over 12.
01:12
And because 0 .12 divided by 12 is 0 .01, then you get 1 .01, just to simplify this a bit to the 12t.
01:23
Now we can take the natural log of both sides...