A professor anticipates having a 30 year career in teaching. She wishes to save some money from each monthly paycheck that will fund the following:

a. An annuity that pays out 30,000 a year for 20 years (paid at the beginning of each year) and

b. leaves a bequest to her university that is a perpetuity-immediate that pays 6000 dollars a year. This perpetuity immediate starts AFTER the annuity in part (a) ends.

Assuming a 6 percent nominal interest rate (converted monthly) for her savings and a 5 percent effective yearly interest rate for her retirement annuity and perpetuity what does she have to save each month?