00:01
So let's say that i want to invest some money when they want to see, um, how long it's gonna take it for it to triple if i have an interest rate of 6% compounded monthly.
00:15
So i'm going to use this formula for a equals p one plus r over and to the anti.
00:32
So i'm here for it to triple.
00:39
I mean, my a two b three times what over? my principle is so i say many friends was one that was gonna be three.
00:49
I'm not gonna right here the one here, though.
00:52
My interest rate reset of 6%.
00:55
So writing that does the decimal over its compound and monthly, so 12 and then i don't know my tears.
01:06
So i'm like, oh, i wanted to see how long it takes to triple, so i'm gonna simple by this a little bit.
01:13
So three equals 0.6 right? 12 is 120.5 so here i'll have 1.5 to the 12 t.
01:28
So now i need to get this 12 t so it's out of exponents.
01:36
Someone take the longer than a both sides.
01:40
I'll take the natural log and so i'm doing this because there's a property of log rhythms that says, if i have, if i have a longer than with something in the exponents, i can take the exponents in front of my lager them.
02:05
So i'm going to do that now.
02:07
National league of three, close 12 t the natural log one point 005 now to get t right itself.
02:21
I'm gonna divide, so i'm gonna underwrite each side by 12 natural log of one point 005 hundreds on the side my twelves will camp slap on my natural logs will cancel out so then i'll have tea equals natural log of three divided by 12 natural log of 1.5 and then i'm gonna plug that in my calculator soon.
03:09
When i do that, i get tea equals 18 point three six years so but then i want to see if it's gonna take a different amount of time.
03:31
If i compound it continuously instead of monthly...