You are a financial planner. Your client's primary objective is to finance her child's undergraduate studies costs. Today is January 1, 2020 and your client found out that your child was admitted to a prestigious five-year graduate program that requires a tuition of $50,000 per year to be paid on January 1 of each of the years 2025 to 2029 (it's a five year very intense program). Regardless of the financing plan that you put into place, you believe it is reasonable to assume your client will earn an average annual return of 10.0% on her investments: she can borrow at 10.0% and/or deposit at 10.0%. This is basically your client's interest rate/discount rate. Suppose your client does not have any money on January 1, 2020. 

a. You advice your client to borrow (at 10.0%) on January 1 of each of the years 2025 to 2029 the amount needed to pay tuition on that day and pay the tuition on that same day. How much will your client owe to the bank on January 1, 2029 after borrowing the last $50,000 on that date? Suppose now your client would be able to get money from her family on January 1, 2020 which she would deposit on January 1, 2020 at 10.0% interest rate. On January 1, 2025 to January 1, 2029 your client would withdraw $50,000 and pay tuition on those specific days. 

b.  How much should your client deposit on January 1, 2020 to be able to make the five payments and have zero balance in the bank account after the fifth payment? 

 

Suppose instead that your client would be able to convince her family to deposit on January 1, 2020 an amount of $45,000 and then for each January 1 of years 2021 to 2024 an amount growing at 5.00% (to clarify, the deposit on January 1, 2021 is 5.00% higher than the deposit on January 1, 2020 and so on, that is, the deposit on each January 1 is 5.0% more than the deposit made on the previous January 1).

  c. Would these deposits be enough to finance the five $50,000 tuition payments (to be made on January 1, 2025 to January 1, 2029)?