00:01
Today, using logarithms and the graph and calculator, we're going to find the time required for each initial amount to be at least equal to the final amount, which is $8 ,000, deposit at 3 % compounded quarterly to reach at least $23 ,000.
00:18
And so what we're going to do is we're going to use our formula for compound quarterly, which is going to be a equals p, which is your principal, which is your starting amount, times one plus your rate divided by your n, which is how many times is being compounded to the nt power.
00:44
And so in order to do this, we have to look through the question and plug in our values.
00:50
And so if it tells you that we are starting with 8 ,000 and the final amount is 23 ,000, we're going to plug 23 ,000 in for a.
00:59
We're going to plug our 8 ,000 in for p, which is our starting amount, which is then going to get multiplied by one plus our rate.
01:15
And so if we look back at our question, we look at our rate is 3 % compounded quarterly.
01:21
And so we convert our percentage of 3 % to 0 .03, which we're then going to divide by 4, since it's being compounded quarterly.
01:32
And that same four is going to be on your exponent to the 4t power.
01:38
And so t is what we're going to solve for.
01:41
And so what we want to do is we want to isolate everything away from the t.
01:45
And so by doing that, we're going to divide by 8 ,000 on both sides.
01:52
When we divide by 8 ,000, those will reduce to 1.
01:55
And we'll do 23 ,000 divided by 8 ,000.
02:00
And so we take our calculator and we do 23 ,000, and we divide it.
02:07
By 8 ,000 and we're going to get 2 .875.
02:14
And so 2 .875 is now going to be equal to this value to the 4t power.
02:24
So we can combine using pemdos and figure out what is inside of the parentheses.
02:29
And so i would do 0 .03.
02:32
We're going to divide that by 4 and then add 1 to that.
02:36
So we're just combining our terms here...