On January 1, 2016, you made an initial deposit of $400 into a savings account to begin saving to pay for 3 years of horseback riding lessons that you plan to begin on January 1, 2021 as well as the purchase of a horse 8 years from now. You will continue depositing $400 on the first day of each month for the next 5 years until you begin the lessons. Lessons will be paid for annually at the end of each year and are expected to increase 3% per year. Your first year of lessons will cost $10,000. At the end of 3 years of lessons, you plan to spend $5,000 to purchase a horse. Your parents have committed to making a 1-time deposit into your savings account 2 years from today. Your goal is for the 3 years of lessons as well as the purchase of the horse to be completely funded by your savings account. No other deposits or withdrawals will be made to your account. The savings account pays a 5% APR with quarterly compounding. What is the minimum amount your parents will need to deposit in 2 years to allow you to realize your goal?

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