00:01
So in this set of problems, we are working with investments and compound interest.
00:06
And the first one, we're doing $50 ,000 invested at 5 .6%.
00:10
It's going to be compounded quarterly for a year and a half, for 1 .5 years.
00:15
And we're first asked, what is the compound amount? now, the compound amount is the same as the future value.
00:23
How much total will have at the end of the time periods.
00:28
All right.
00:30
And so the formula here is that the future value is the present value times one plus r, i'm going to call it r star, raised to the t star.
00:46
Where r star is going to be our rate, written as a decimal, 0 .056, but it's compounded quarterly.
00:58
So there's four quarters in a year, so i've got to divide that by four.
01:01
So it's the adjusted rate or the rate per period.
01:07
And then t star will be the number of periods with that same formulation.
01:13
So this is 1 .5 times 4, which is going to be 6.
01:19
And so the future value here, the compound amount, is our present value, our $50 ,000 times 1 plus .056 divided by 4.
01:34
To the sixth.
01:37
So in our calculator we take 0 .056 divided by 4 and add 1 to it.
01:54
And so this term in here is 1 .014.
01:59
We raise that to the 6th times 50 ,000 and we get 54 ,000 three hundred forty nine dollars and seventy seven cents.
02:22
Now we're we're also asked how much compound interest do we get.
02:33
Well, everything above and beyond what we initially invested is the interest that we earned.
02:40
So we take 54349 .77.
02:47
I'm going to clean that up because that's a four, not a nine.
02:50
Minus the 50 ,000 gives us $4 ,349 .77.
03:04
So there's our compound interest that we earned on this.
03:13
Okay, problem two has two parts, a and b.
03:19
And we're asked for the compound amount when we invest $43 ,250 invested at $9 ,000.
03:34
Invested at 9 % compounded monthly 10 years.
03:53
So again we use the same formula...