TVM funding an annuity due (Practice Problem)

[Akeg]

Hello,
If someone can please help me grasp this problem it would be much appreciated. The worked out solution is using the 10% ROR as an interest rate for the 5 year annuity due. I fail to understand why the 10% is being factored into the five annual payments. Isn’t the question simply stating that the 10% ROR is on the 3 year investment account and not an interest rate of the 5 year annuity due?
QUESTION
Suppose you must make five annual $1,000 payments, the first one starting at the beginning of Year 4 (end of Year 3). To accumulate the money to make these payments, you want to make three equal payments into an investment account, the first to be made one year from today. Assuming a 10% rate of return, what is the amount of these three payments.
My Solution
FV=$5,000 I/Y=10% N=3 PMT=-$1,510.57
However according to practice problem, the answer is as follows
1.)N=5 I/Y=10 PMT=-1,000 PV3=$4,169.87 (BGN MODE)
2.)N=3 I/Y=10 FV=-4,169.87 PMT=$1,259.78 (END MODE)

 

[S2000magician]

You’re neglecting the interest earned on the account from the first payment to the last.
Draw a time line.

 

[Tartaglia]

The 10% also needs to be factored into the 5 annual payments starting at t=4, because you are interested in their present value and in order to get that, you need to discount them back to today. The question does not explicitely state this fact, but you have to bear in mind that in order to compare any cash flows from different periods, you need to compute their value at one point in time (typically today).
Try to explain the following question to yourself. Say you buy a car today for $10,000 and the dealer gives you a choice of paying it right now or in years from now. Which one would you choose?