The finance director of Sapphire Distributors estimates that his company will have to spend $312,000 on a new machinery in three years from now. Two alternative methods of providing the money are being considered, both assuming an annual rate of interest of 8%.

a. A single sum of money, $X, to be set aside and invested now, with interest compounded every six months. How much should this single sum be, And what is the effective annual rate of interest?

b. $Y to be put into a reserve fund every six months, starting now. If interest is compounded every six months, what should $B be, in order that the $312,000 will be available in two years from now?

c. The company has also decided to set up a fund for its employees with an initial payment of $3,212 which is compounded three monthly over a five year period at 4.5% per six months. Required:

i. Calculate the size of the fund to two decimal placed at the end of the four years.

ii. Calculate the effective annual interest rate, to two decimal places.