TVM question - 2 interest rates in Question

CFA Level I Quant
#1

Hello,

Q: Couple is saving for child’s tuition for 4 years starting 18 yrs from now. current annual cost of college is 7K, and is expected to rise at an annual rate of 5%. In planning, couple assumes they can earn 6% annually. How much must they put aside each year starting next year, if they plan to make 17 equal payments?

I understand finding the future value of each tuition payment at 18, 19, 20, and 21, and then using the PV formula to equate the tuition payments back to t = 17, BUT shouldn’t the rate used for the PV formula be 5% to find the PV of the tuition payments at t = 17??? The book uses 6%, but my understanding is that is what the couple CAN earn, but what they NEED is what tuition will actually cost and in that case it will only rise by 5%.

Please let me know where I’m missing something. Thanks for any help you can offer.

#2

As they can earn 6% p.a. during the 4 year university time the money they need to have saved in year 17 (=PV of annual payments during the 4 years) is less. It would be more if they could earn only 5% - but the text explicity says that they can earn 6% p.a.

#3

Oh wow, it just clicked. So because they can earn 6% while child is at school, I can use that 6% rate to discount each payment back to t =17. Thank you very much for your help Oscar! It is much appreciated.

#4

Plus the 5% is used to determine what the actual dollar amounts needed at times 18 to 21 will be.