Suppose you plan to retire early on your 50th birthday and to start withdrawing from your retirement savings when you turn 51 years old, but have $10,000 left over when you reach the age of 90 years old. 

Assume that:  You are 20 years old today and you want to have a retirement plan until you are 90 years old.  

• Your retirement savings earn 3% per annum.  
• The discount rate of 3% per year remains unchanged until your 90th birthday.  
• You require $60,000 per year after turning 50 years old until your 90th birthday.  
• To meet your retirement goal, you plan to deposit each year (at the end of each year) until you turn 50 years old (the last deposit is on your 50th birthday). 

a. Draw a timeline showing your retirement plan above.  

b. Calculate your retirement savings balance at your retirement age (your 50th birthday) to meet the retirement plan above.
c. How much would you have to deposit each year until your 50th birthday to meet your retirement goal?