Question 7 (EAR vs APR: 15 points) Annuity Assume that you are planning to save for the education for your child. You want to let your child study in US when he gets to high school at the age of 15 that is exactly 10 11 Period years from today. You expect your child will stay and study overseas for 7 years. You estimate that he needs to withdraw $400,000 per year for 7 years beginning on his 15th birthday to cover tuition and living expenses. You intend to invest in a mutual fund which offers 9% APR compounded semi-annually. (a) If you have decided to make one lump sum payment today to get enough money for your child, how much should you invest today? (b) If you make semi-annual contribution starting six months from now, how many contributions will you make? How much should you invest each time? Assume that you will make the last contribution when your son turns 15