A woman wants to prepare for retirement. On her 25th birthday she begins making monthly deposits of $Y into a fund which earns an annual effective interest rate of 8%. The last deposit is one month prior to her 65th birthday. On her 65th birthday she uses the fund to purchase a 30-year annuity-due which pays $X each six months for 10 years, and $2X each six months for the remaining 20 years.
(a) Write an expression for X/Y in terms of annuity symbols based on an the 8% effective annual interest rate.
(b) Write an expression for X/Y in terms of annuity symbols based on effective interest rates for time periods which correspond to the payment periods.
(c) Calculate X/Y