Problem $2$

Steve is a newborn. His parents are planning to contribute $$6,000$ a year $($or possibly less$)$ towards his college fund into

an account that will grow at a constant rate of $5\%$ a year. Both parents work for the same company that offered to match

parental contributions dollar for dollar for the first $6$ parental deposits and $25$ cents for every parental dollar for

subsequent parental deposits, until Steve reaches $19.$ Once he reaches $19,$ both the company and parents stop their

contributions. College costs are expected to be $$55,000$ a year and Steve spends $4$ years in college once he reaches $19.$

Assume that the beginning account balance is $$35,000($a$)$ What is the smallest amount parents should contribute

each year to make Steve's college affordable? Complete table below and solve the problem $(15$ points$).$