This Question has been answered but im looking for some more clarification. Can someone please answer this and explain to me every step they are doing and why. I Dont understand why we factor out the 7.5% from the price of each year of college. Wouldnt it not correlate with the account earning 7.5% because they are different values? Please explain thank you!

A father and mother are planning a savings program to put their daughter through college. Their daughter is now 8 years old. She plans to enroll at the university when she is 18 and it should take her 4 years to complete her education. Currently, the cost per year (for tuition, etc.) is $16,200, but a 2 percent inflation rate in these costs is forecasted. The cost for each year of college will be withdrawn when she turns 18,19,20, and 21 . The daughter received $13,000 at age 4 and another $2,900 at age 6 from her grandmother; this money, which is invested in an account earning 7.5 percent interest compounded annually, will be used to help meet the costs of the daughter's education. The rest of the costs will be met by money the parents will deposit in the savings account. They will make 4 equal annual deposits to the account, with the first deposit being made today on her 8th birthday and the last one being made on her 11 th birthday. These deposits will also earn 7.5 percent interest compounded annually. How large must each deposit (from the parents) be in order to put the daughter through college? (Round cash flows to nearest dollar throughout.) a. $5,126 b. $4,629 c. $4,103 d. $5,657 e. None of the above is within $10 of the correct