Barbara currently has $25,000 in her RRSP. She plans to contribute $4,000 at the end of each year for the next 30 years and then use the accumulated funds to purchase a 25-year annuity making payments at the end of each month.

In 30 years, the fund from which the annuity is paid will earn 4.5% compounded monthly. What monthly payment will she receive?

How much should Barbara put away monthly, at 8.2% per annum, compounded monthly, so that she can still be guaranteed the same monthly payments from the 25-year annuity derived in part (a)?