We use Formula F when the account value is increasing over time. 

We use Formula G when the account value is decreasing over time. 

A down payment is an initial payment towards a loan. It is paid out of pocket (and there is no interest paid on this amount). 

You can think of the down payment as reducing the loan amount. For example, if you are purchasing a car for $25,000, you may make a down payment of $5,000. This means that you only need to get a loan for $20,000.

The principal is the amount that you borrow for the loan. 

In the example above (in the down payment question), the principal would be $20,000 (since that's the amount you need to get a loan for).

Amortizing a loan means that you are eliminating (or paying off) the loan. 

Payments are set up so that each payment is the same amount. As time goes on, the amount of each payment that goes toward interest decreases, and the amount of each payment that goes towards principal increases.