00:01
Hello, welcome to this lesson.
00:03
In this lesson we are looking at the future value of an annuity.
00:07
So this typical question you make a deposit of $1 ,000 every six months into an account where it earns $30 .5 compounded semiannually.
00:22
So we are looking at how much interest you would have in one year.
00:27
So we can look at the value of this savings after one year, then we can subtract it from the actual deposit that you have made in order to get the interest.
00:41
So let's go on.
00:44
We have the f being as the future value, which we are looking for.
00:55
We have the r as the rate.
00:58
The rate was given to us as 3 .5%, but this compounds annually twice.
01:06
So we are looking at an effective rate of 0 .035 divided by 2, which is 0 .0175.
01:25
The next one is the number of compounding times.
01:29
So compounding times in the whole year, it compounds twice.
01:38
So compounding times.
01:48
So this compounds twice in a year.
01:50
We are looking at in a year.
01:53
So the future value is equal to the $1 ,000 1 plus the rate, which is 0 .0175 to the power n, the number of compounding times minus 1, all over 0 .0175.
02:14
So the value at the end of the year would have 1 plus 0 .0175.
02:27
This is 2 to the power 2, then minus 1...