Future value and present value. I have some more questions

Water Cooler Investing
#1

Again, some FV become PV and it’s getting me confused. Example:
Mr X wants to retire 30 yrs from today, with an income of $30,000 per year and lasting 20 years. He also wants to purchase a vehicle that will cost $50,000 in ten years. Mr X can only save $4000 a year for the next 10 years. How much must he save to accomplish both objectives. All investments will earn 7%

Step 1. I=7; payment -30,000;N20 PV…is what we are looking for because we need to know how much he will need today to get $30,000 a year… right ?

Step 2. Payment -4000; I 7; N10; FV is what we are looking because we need to know how much her 4000 a month will be in 10 years… which is $ 55,265.79

He will have $55,265.79 in ten years to buy the car minus the cost of the car which is $50,000

In 10 years he will have saved up after the car purchase $5,265.79

THIS IS MY QUESTION …

Why do I need to calculate the FV of $5,265.79??

Step 3 calculating FV of 5,265.79 which is what I’m confused about.
PV 5,265.79; N20; I 7; FV? Answer is $20,376.95

But why do I need this calculation…? Everything after this I get.

The answer is $7,255,52 / month is what he needs to save.

Please help :sweat_smile:

#2

Mr X plans to purchase the car 10 years from today. At that time he would still have 20 more years for retirement. So the balance that he would save after purchasing the car i.e. $5,265.79 would be further invested for 20 years to create the corpus he needs when he retires.

#3

Just to clarify, in step 1, the PV is as of the date of retirement, not today.

ETA: And should that be $4,000/year for the first 10 years and $7,255.52 for years 11-30?

#4

Because you still have 20 years to invest prior to drawing on the assets.