Gurpreet deposits $8,000 into Fund X that pays monthly interest at a nom-

inal annual rate i(12) = 2:4%. At the end of each year, Gurpreet withdraws

all the interest earned in that year, plus $1,000 of the original investment

(so Fund X is exhausted at the end of year 8), and deposits into Fund Y

earning an effective annual rate of 1.75%.

a) Prove that Gurpreet's deposits into Fund Y form an arithmetic annuity

with initial deposit P and increment Q. Find P and Q.

b) Calculate the amount of money in Fund Y at the end of 8 years.