Caity and Peter are best friends who are concerned about saving for their future, so they have decided to both open a bank account each and start saving. They have decided to retire in 40 years. Once they have retired, they will each need $100,000 per year for 20 years. After 20 years, they will enter a retirement home together for the remainder of their lives. As soon as they enter the retirement home, they will need to make a single payment of $350,000 each (this occurs exactly a year after the last $100,000 cash flow).

Given they want to have exactly the same amount in their bank accounts at retirement, and that interest will be fixed at 8% p.a. compounded quarterly for their entire lives, how much do Caity and Peter have to deposit monthly into their savings accounts? In addition to this, you are given the following information:

The first withdrawal of $100,000 is at t=41;

Peter expects to receive an inheritance of $65,000 at t=15, which he will deposit into his savings accounts;

Caity is expecting to get cash bonuses of $4,000 every year for 10 years, with the first bonus occurring at t=1 (which will all be invested into her savings account); and,

All payments are made at the end of the year.