Vicky Sterling is currently $30$ years old and decides to start saving for her retirement. Her current $($annual$)$ income is $35,000$ and will grow at a constant rate of $2\%$ annually until her retirement. She would like to save one quarter of her net income every year from next year onwards until she turns $60($including that year$).$ She agrees with the bank on annual interest rate compounding at an annualized interest rate of $4\%.$ The final value of her savings account come closes to:A$)575,000$ B$)600,000$ C$)625,000$ D$)650,000$