00:02
And this problem says if $2 ,500 is borrowed at 4 .5 %, find the amounts due at the end of three years if interest is compounded first annually.
00:14
And so in my formula, you can use this formula for annual.
00:23
It just simplifies down really easily.
00:27
So in the formula, your r is right.
00:30
You're in as a number of times.
00:31
It is compounded per year.
00:34
And so if you're compounding it annually, then that's once per year.
00:38
Your a -0 is your initial rate, your initial value.
00:44
Your a is your final value.
00:47
And then you can use that formula to calculate.
00:56
Now, with this formula, you're going to get final value that is owed after three years.
01:02
And so just remember the question asked, i want to make sure it says find the amounts due at the end of three years.
01:11
Okay, so if it asks for the amount of interest instead of the amount due, then you would just need to subtract to get your interest amount.
01:21
Okay, so for annually, we're going to say on that first one, a is equal to a sub zero, which we barred 2 ,500 times 1 plus r, which is going to be 0 .045 over n, which is 1, raise, to the n t so n is 1 times t is 30 and so you get 2 500 times 1 .045 to the third power and then you just need to take and plug that into your calculator and so the 1 .045 raised the third power is 1 .41166125 and then when you multiply that times 2 ,500 you're going to get $2 ,852, and it's .915, so that would be $92.
03:01
And so it's to me like they're going to be paying $352 .92 on that if it's compounded annually for three years.
03:14
So in part two says, what if we compound it quarterly? and so again, we have a is equal to a sub -0 times 1 plus r over n raised to the n -t power.
03:50
Okay, and so a is going to equal your a -sub -0, which is $2 ,500 times 1 plus your r was 045 over n.
04:05
And remember, it's a number of times compounded annually.
04:08
So if we're going to do this quarterly, quarterly means four times a year.
04:14
And so then times nt, so that would be four times 30.
04:21
And again, you just got to get that all plugged into your calculator.
04:42
I get $2 ,859.
04:48
And 0 .186 would make 0 .19.
04:51
So 19 cents.
04:59
Then part three says monthly.
05:16
And so you're going to have your a as equal.
05:19
To 2 ,500 times your 1 plus your r, which is 0 .045 over n.
05:29
And if we're going to do monthly, there's 12 months in a year, so that would be over 12, raised to the 4 times 12.
05:37
Sorry, i'll try that again.
05:43
Raise to the n -t and m -s -12.
05:46
T is 3.
05:54
Again, plug it into your calculator.
05:56
And you get $2 ,860, and that's .619, so .62, so 62.
06:22
So, $0 .42.
06:22
Part 4 says weekly.
06:36
52 weeks in a year.
06:38
So a is going to equal $2 ,500 times 1 plus 0 .045 over n, and there's 52 weeks in a year.
06:49
That's how many times you're going to go compounded a year, times in, a raise to the end, times t power.
07:05
Plug that into your calculator.
07:22
We should get 2 ,861 .17.
07:31
So, 17 cents.
07:37
And then we go to daily, and there's 365 days in year.
07:46
So a is going to equal $2 ,500 times.
07:53
1 plus 0 .045 over 365, raised to the nt, so 365 times 3.
08:27
I get $2 ,861 .31 .32.
08:41
Then 6 says hourly.
08:45
That's one i don't know off the top of my head...