How is it a ? why are they not using beg mode when discounting

[Girish54]

[guest]

It doesn’t really matter what year you call year 0 for the discounting.
You pay 100,000 now, x a year for years 1 to 5, and then receive 55,000 a year for years 6 to 9.

100,000+x\sum_{n=1}^{5}1.06^{-n}-55,000\sum_{n=6}^{9}1.06^{-n}=0

solve for x

x=\frac{55,000\sum_{n=6}^{9}1.06^{-n}-100,000}{\sum_{n=1}^{5}1.06^{-n}}=10,068.71

If you do what they do and say that the start of her college career is year 0, then
You pay 100,000 in year -6, x a year for years -5 to -1, and then receive 55,000 a year for years 0 to 3.

100,000\ast 1.06^{+6}+x\sum_{n=1}^{5}1.06^{+n}-55,000\sum_{n=0}^{3}1.06^{-n} =0

If you multiply through by 1.06^{-6}, you get the same result as before

[AKRapoza]

Excuse the sloppy penmanship, but this is how you solve it.

You start by figuring out the present value of the four tuition payments. In my work here, I used Beginning mode to get to the present value at the beginning of T6, but in the solution given, they don’t use beginning mode. You don’t necessarily need to use beginning mode, but I find it easier that way. Just remember that the end of year 5 is the same thing as the beginning of year 6.