Im having some trouble with a pension fund question that has a lot of variables and a seemingly complex formula.

Joe is a qualified Actuary. On Joe’s 30th Birthday he signs an indenture (essentially an employment contract) to immediately start working for Munich Re (one of the world’s largest re-insurers). The indenture stipulates that Joe will work for Munich Re until the legal Retirement Age of 65 However, if Joe would like to retire early, he can retire at the Early Retirement Age of 59.

You can assume that Joe will not die whilst working for Munich Re and Joe will retire early at the age 59 (i.e. on Joe’s 59th Birthday he will retire). In addition, you may assume that Joe will not quit or be fired.

Munich Re has decided that Joe will start on an initial annual salary of 775 300 and Joe’s annual salary will be increased at the end of each year of service, provided that he is not retiring. His annual salary will then be broken up into 12 equal monthly salary (MS) payments. Munich Re also deducts any monthly pension fund contributions (PFC) and any income tax (IT) that needs to be paid before paying Joe his net monthly income.

Joe’s initial annual % increase in salary is 7.5%. Joe will receive 5 annual salary Increases at the rate 7.5% after which his annual % increase in salary will changed to 5.75%.

Munich Re has also set up a special type of pension fund for Joe. Joe will make payments into the fund, so that he will have a pension when his contract ends.

Joe has decided that he will pay a fixed percentage equal to 10% of his monthly salary into the Defined Contribution Fund until he retires.

Munich Re has also decided to make additional payments into the Defined Contribution Fund for Joe. These are:
-An annual bonus at the end of each year of service, where Munich Re will deposit an amount equal to Joe’s Last Monthly Salary multiplied by a factor of 1.2
-In addition, when Joe retires he will receive a retirement Bonus. Munich Re will deposit an amount equal to the number of years of service (29) multiplied by his current Annual Salary multiplied by Retirement Bonus Factor of 0.0525. i.e. AS*NYS*RBF into the pension fund on retirement.

Munich Re has set up the Defined Benefit Pension Fund so that interest accrues at the end of each month. In addition, Munich Re deposits an initial amount of 100 into the Pension Fund when Joe sign’s the Indenture. The fund is set up so that the first 3 years the fund grows at a monthly effective interest rate of 1.1%. After which the fund grows at a monthly effective interest rate of 1.325%.

What is the value of the Pension Fund, a month before Joe reaches the legal retirement age?
What is the value of the Pension Fund when Joe's reaches the legal retirement age?

I know its a lot of reading and thinking but its giving me a lot of problems. I'd really appreciate any help regarding the equation. I can think the problem through and know what needs to be done, I'm just unsure of how to go about it and the formulae involved.

You could ask Joe. He IS a qualified actuary.

This whole problem requires tedious attention, not difficult mathematics. Break out your spreadsheet. That would be the easiest way to track all the streams.

This is a hard work and careful attention problem. No one can do it for you.