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% interestcompounded 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 $Rat the end of each period foryyears and that there arempayments per year. If the interest rateris compoundedctimes in a year (for anyc>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, withR= 4000,r= .08,m =2,y= 10 andc= 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.