00:01
In the given question we are told that francine currently has an amount of $65 ,000 with her.
00:09
She has an amount of $65 ,000 in her 401k account at work and she plans to contribute $9 ,000 each year for the next 15 years.
00:23
So this is the current amount that she has.
00:30
And we are told that she is going to contribute $9 ,000 each year, each year for the next 15 years.
00:43
For the next 15 years.
00:48
For the next 15 years.
00:56
And what we are told to find is how much will she have in the account in 15 years if the account averages a 7 percentage annual return so the annual return is given to us as 7 percentage so what we could do over here is we can first find the future value of what she already has in her account right that is let's just write in order to find the future value what we do is the future value is equal to the present value times 1 plus r raised to the power of n.
01:40
So over here what we would have then is the present value is what we call the current amount that we have so it is 65 ,000 times 1 plus r would be the interest rate.
01:57
So over here we are going to take r as the annual return percentage, right? so, when we take r, we should take it as the decimal number.
02:10
So 7 percentage is 7 divided by 100 which is 0 .07, right? so this is what r is equal to.
02:20
So 0 .07 and n is the period that we are keeping this amount for.
02:29
So, the period, the period that we are keeping this number for, this amount for, is 15 years.
02:41
So here there would be 15 and this would give us the future value of the amount, 65 ,000, in 15 years, right? so when we take 1 plus 0 .07 and take the power of this number as 15, and then multiply it with 65 ,000 what we get over here as the result which is the future value is let's just look over here it is equal to 179 ,000 179 ,000, 337 .05.
03:27
$0 .5...