1- John and Sarah married 12 years ago. Today is their daughter Alices 10th birthday. Alice is a very clever girl and her parents think that it is time to plan for her higher education. Alice is going to a school with an IB program so she can go to the USA for her university education. John has already done his research and learned that today tuition fees and other living expenses in the USA costs $50,000 per year. Unfortunately, this value increases with inflation, and the USAs inflation rate is 2% per year. Alice wants to study business. She will attend the university on her 18th birthday and will study for four years. The payments should be done at the beginning of each year. John and Sarah want to save the total amount needed for Alices education on her 18th birthday. They want to save certain amount every month for Alices education and invest in a bank account. They talked to a bank manager and learned that they can earn an interest rate of 10% compounding quarterly. They will make the initial payment today and the last payment will be done when Alice starts university. During Alices 10th birthday party Sarah talks about their plans related to Alices university education to her parents and in-laws. Grandparents also want to contribute to Alices education. Her maternal grandparents want to give $750 every six months and her paternal grandparents decide to give $400 every quarter until Alice starts university.

a. Calculate the total cost of Alices university education when she is 18 and starts the university

b. Calculate the amount John and Sarah should save every month for Alices education after taking into account the amounts given by the grandparents.