Quant Methods Annuity

[mineral]

Suppose you plan to send your daughter to college in 3 years You expect her to earn 2/3 of her tuition payment in scholarship money, so you estimate that your payments will be $10 000 a year for 4 years. To estimate whether you have set aside enough money, you ignore possible inflation in tution payments and assume that you can earn 8 percent annually on your investments. How much should you set aside now to cover these payments?
I ended up getting an answer of $26 292.77. The answer is $28 396.15 It seems I have discounted one period too far. However I do not understand why they only discount the original figure backwards by 2 periods, not 3? (as you have to send your daughter to college in 3 years, not 2).
Any help would be fantastic. Thanks

 

[Oscar]

Draw a timeline at first.
If you discount the $10,000 starting with year 3 for four years assuming your calculator in in END-Mode you get the PV of the payments at the beginning of year three ($33,121), which is equal to the PV at the end of year two.
Recall that the END-Mode assumes year and payments. Hence, for getting the PV at year 0 you only need to discount back by 2 years, not by 3. Alternatively you could change to BGN-Mode and discount 3 years. Although more time consuming the result will be the same ($ 28,396).
Regards,
Oscar