00:01
Hi, in this question, we're looking at compounding interest.
00:05
So the formula for compounded interest is given here.
00:10
So it basically says that the amount you have is equal to the amount you invested p, in this case, 10 ,000, times 1 plus r, which is the interest rate, over n, which is number of compounds per year, to the power of n times t, where t is the number of years that you leave your money in this account.
00:45
So everything in here we already know.
00:48
So we know we invest 10 ,000.
00:50
The interest rate is 5%.
00:52
And we leave it for either 10 or 30 years.
00:57
The only thing we don't know is is n here.
01:02
So the number of compounds per year is what we're sort of changing.
01:06
So if we compound annually, this is the same as saying n equals 1.
01:14
So then our formula becomes a is equal to 10 ,000 times one plus 0 .05 over one, one times 10.
01:26
So this is for the 10 year case.
01:29
And if we do this, we get $16 ,000, $288, or sorry, $16 ,288, and about 95 cents.
01:47
Right, so this is 10 years.
01:49
And then 30 years is basically the same.
01:54
One plus 0 .05 over 1.
01:57
Except now we raise it to the 30th power.
02:04
And so naturally this should be a lot more, and we get $43 ,219.
02:10
And 42 cents...