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.