00:01
In the given question we are told that you want to be able to withdraw $45 ,000 from your account each year for 30 years after you retire.
00:12
So let's write this down that you need to withdraw.
00:21
You need to be able to withdraw, able to withdraw 45 ,000, 45 ,000.
00:35
For each year, each year, for 30 years after you retire.
00:48
30 years after you retire.
00:52
So this is what we wish to be, wish to have in our bank account, right? we need an amount so that we can withdraw 45 ,000 each year from this account for 30 years after you have retired.
01:08
Now we are also told that we are expected to retire in 15 years.
01:14
Expect to retire in 15 years.
01:21
In 15 years.
01:25
And we are asked to find the amount that we need to deposit each year under the retirement so that this is possible.
01:34
And we are told to take the interest earned.
01:38
By the account interest earned interest earned by the account to be five percentage so what we can first do over here is let's calculate the amount that the account would need to have for this to for this to be possible right so let's use the formula which is the present the present value the present value annuity is equal to the periodic cash flow that happens in the account, which over here would be 45 ,000 that we withdraw each month, times 1 minus 1 by 1 plus r raised to the power n, divided by r, where r is what we would say as the rate, of r is the rate of the compounding period, rate of return of the compounding period, rate of return for the compounding period.
02:57
So this rate of return in the compounding period for us is what we have been told to take as 5 percentage.
03:07
So we can take this as 5 percentage which is equal to 0 .0...