I have a question of an annuity calculation..

My math professor gave me this question to solve:

If Tom contributes $4000 at the end of each semiannual period (**semiannually)** into a retirement account with 8% interest **compounded quarterly,** and he continues these semiannual payments for 10 years, I know that he will have $119,607.89 in his account, as opposed to the $119,112.31 that he should have if interest were compounded semiannually.

Suppose that Tom contributes $*R* at the end of each period for *y* years and that there are *m* payments per year. If the interest rate *r* is compounded *c *times in a year (for any *c* > *m*), __write the future value of this financial scheme as an algebraic function of R, m, y, r and c.__

You’ll know that you have the right answer if you can use your formula using the information in the scenario above, with *R* = 4000, *r* = .08, *m = *2, *y* = 10 and *c* = 4.

If someone can help me with the solution it will be greatly appreciated. I can't seem to grasp this whole annuity thing. He gave me 2 hints saying that:

1. Push forward the first few payments to the end of term value using the compound interest formula.

2. Know what a monotonic polynomial is.