00:01
So we want to know how long it's going to take to triple our investment.
00:03
If we start with i and end up with 3 times i, we want to know how long it's going to triple if it's invested at 4 % and it's compounded monthly.
00:13
So we take our investment times 1 plus .04 over 12, and then that's going to be to the power of 12 times however many years, and that's going to equal the 3 times that investment.
00:27
So we'll have that 1 plus .04 over 12 to the 12y power, and that will equal 3.
00:36
Then we can take the log of both sides and whatever base you choose.
00:40
I'll use natural log, and then we can use log of the power, and then finally we can do a division to get y is equal to the natural log of 3 divided by, and then we'll have a 12, and then the natural log of that 1 plus .04 over 12.
01:02
And i'm going to put that into my calculator right now.
01:05
So natural log of 3, and again, put a left parenthesis when you enter this into your calculator here so that i can do natural log of 3 left parenthesis, and then 12 natural log of 1 plus .04 divided by 12.
01:22
And don't round that value off.
01:25
And it comes out to be that it will take 27 .51 years, so about 27 and a half years.
01:32
Now, on the other hand, if we have it compounded continuously, then we have that i times e to the negative, and the rate is .04 to the time...