Business Finance Help Please?

In their meeting with their advisor, Mr. & Mrs. Smith concluded that they would need $40,000 per year during their retirement years in order to live comfortably. They will retire 10 years from now and expect a 20 year retirement period. How much should Mr. & Mrs. Smith deposit now in a bank account paying 9 percent to reach financial happiness during retirement?

Any help would be great I am totally stumped on this question. I was thinking of taking the 40,000 a year * 20 since that will be there retirement lifetime.
Then do the PV of 800,000 but that didnt seem right

I think you solve this by going forward to the start of their retirement and getting the Present Value of that retirement stream.

Then you solve for the present value today of the number obtained above - which is input as a future value over 10 years.

The only problem is whether the payment occur at the beginning or end of the periods.

Assuming the payments are at the beginning of the periods, here is how the calculations shake out:

Present value (at year 10) of receipts of $40,000 per year for 20 years at nine percent interest = $365,141.

Then, taking that amount as a future value in year 10 and obtaining the present value of that 10 years earlier: = $154,239 is the amount to deposit today to begin the planned retirement withdrawals 10 years in the future.

You need to keep in mind that since they will be depositing the money today that it will begin to grow immediately. This question will require two parts. The first part deciding how much the money will grow in 10 years and then how much the money will grow for the last ten years as it's being depleted. Also, you will need to know if the return will pay interest annually, semi-annually, quarterly, weekly, etc.

You're on the right track, but remember the money will only be able to grow 10 years before it starts being depleted.