Problem 2. Financial Planning,

You are a financial planner. Your clients primary objective is to finance her undergraduate studies costs. Today is January 1, 2022 and your client found out that she was admitted to a prestigious four-year undergraduate program that requires a tuition of $40,000 per year payable on December 31 of each of the years 2022 to 2025. Your client does not have any money on January 1, 2022. 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 (can borrow at 10.0% and/or deposit at 10.0%). This is basically your clients interest rate/discount rate.

a. Strategy One: You advice your client to borrow on January 1, 2022 from SLS Bank (Student Loans Support Bank) an amount, call it L, and instruct SLS Bank to make the four tuition payments out of the loan contracted when they are due (as described above, i.e., $40,000 per year payable on December 31 of each of the years 2022 to 2025). i. What is the amount L that your client has to borrow on January 1, 2022 such that the four tuition payments are covered when due? ii. You advice your client to repay on December 31, 2025 the whole amount that your client owe to the bank as of December 31, 2025 after the last tuition payment is made. How much is that repayment amount? For the following two questions you can assume that the amount your client owes to the SLS Bank as of December 31, 2025 is $200,000.

b. Strategy Two: You advice your client to repay a constant amount, call it A, on December 31 of each of the ten years starting with December 31, 2026 such that after the total of the ten repayments the client does not owe anything to the bank. Find A.

c. Strategy Three: You advice your client to repay an amount $30,000 on December 31, 2026 and then to grow the repayment amount at a growth rate of 2.00% per year for each starting with December 31, 2027 (to clarify, the repayment on December 31, 2027 is 2.00% higher than the repayment on December 31, 2026 and so on). Does the client still owe anything after the total of the ten repayments (underpay) or would the client pay too much (overpay) under this proposed repayment strategy?