0:00
All right.
00:01
So the question that we're going to be looking at today is it asks a sum of $3 ,000.
00:06
So we're going to go, $3 ,000, is placed in a savings account at 6%, 6 % per annum.
00:20
How much is in the account after one year if the interest is compounded? and we have to sell for three different ones.
00:26
So first we need to solve if the interest is compounded, a, annually, b, semi -annually, or c, daily.
00:35
So, obviously, as with all these questions, we are going to use the formula.
00:42
A is equal to p1 plus 1 plus r to the power of n.
00:53
So first, we are going to solve for a, which is annually, if the interest is compounded annually.
01:03
So, to do that, we are going to start with a is equal to 3 ,000, which is our principle, 1 plus the 6 % to the power of 1 because it's only compounded once.
01:19
So this is equal to 3 ,000 1 plus, oh, sorry, 1 .06 to the power of 1 .06.
01:35
And when you put this into your calculator, it is equal to 3 ,008.
01:43
So your amount if it's compounded annually is 3 ,108.
01:54
So that is for compounded annually.
01:57
Next what we're going to do is we are going to solve for when it is compounded semi -annually.
02:05
So that's two times a year.
02:07
So now what we have is a is equal, oh, sorry, to stop the confusion, i will write semi -annually here, semi -annually.
02:24
So now we're going to use our formula once again.
02:27
So a is equal to still 3 ,000.
02:31
But now something different happens with the interest rate.
02:37
And the interest rate now has to be 0 .06 divided by 2 because it is compounded twice in twice per year...