00:01
So in this question, we have an initial amount p, an annual interest rate r and a time t given.
00:10
And we want to find the future value of the investment when the interest is compounded annually.
00:17
So if the interest is compounded annually, what's the formula? the formula is a equals p times the quantity of 1 plus r being raised to the t power.
00:31
So here they say that my p is 5500.
00:36
My r is 2 .85%, but i have to convert that into a decimal.
00:46
When i convert that into a decimal, it becomes 0 .0285.
00:52
So i move the decimal over twice.
00:54
The 2 .85 % becomes 0285.
00:59
And then my t is five years.
01:03
And so i go to my calculator, $5 ,500 times the quantity of 1 plus .0285 being raised to the fifth power, getting $6 ,329 .72 cents.
01:19
$6 ,329 .72.
01:24
In b, what if the investment is compounded, much? monthly.
01:34
If we compound more than once a year, the formula gets amended a little bit.
01:40
It's a equals p times the quantity of 1 plus r over n raised to the nt power.
01:50
So n is the number of times per year that the interest is compounded.
01:55
So that's going to be 12 this time.
01:59
My p stays the same, so still 5 ,500 times the quantity of 1 plus r.
02:07
R is 0 .0285 over n, n is 12, raised the power of n times t, raised the power of 12 times 5.
02:21
So i go to my calculator 5 ,500 times the quantity of 1 plus 0 .0285, and that's being divided by 12, i think we said, being raised to the power of 12 times 5.
02:40
And now i get 60 .000.
02:42
$6 ,341 .27.
02:46
$6 ,341, and $27.
02:52
And then in c, now we're going to compound daily.
02:58
So how many times per year are we compounding? well, i'm using the same formula, but n again is the number of times per year that you compound.
03:11
So my n here is 365.
03:13
And so what does this give us for our formula? a equals p is 5500 times the quantity of 1 plus 0 .085 over 365, raised to the power of 365 times 5.
03:42
And so what do we get? we've got 5500 times the quantity, 1 plus 0 .0285.
03:52
5 divided by 365, raise the power of 365 times 5...