Samantha Scholl is planning to save for her sons university education. Her son is currently 11 years old and will begin university in 7 years. Samantha has an index fund investment of $17,500 earning 9.5 per cent annually. Total expenses currently at Lincoln University where her son says he plans to go, are expected to be $35,000 per year. Samantha plans to invest a certain amount in an investment fund that will earn 11 per cent annually to make up the difference between the education expenses and her current savings. In total, Samantha will make seven equal investments with the first starting today and with the last made a year before her son begins university.

a. What will be the present value of the 4 years of education expenses at the time Samanthas son starts university? Assume a discount rate of 6 per cent.

b. What will be the value of the index fund when her son just starts university?

c. What is the amount that Samantha will have to have saved when her son turns 18 if she plans to cover all of her sons university expenses?

d. How much will Samantha have to invest every year in order to have enough funds to cover all her sons education expenses?