An annuity certain with payments of $500 each at the beginning of each quarter, for a certain number of years, is to be replaced by an annuity with the same present value and lasting for the same number of years, but with payments at the end of each month(Let's call this X) instead. Calculate the new monthly payment correct to the nearest cent, assuming a constant annual force of interest of 0.06.
I know that 500 multiplied by the formula for an annuity due with interest rate (e^(0.06/4)-1) and 4n payments is equal to X multiplied by the formula for an annuity immediate with interest rate (e^(0.06/12)-1) and 12n payments. However, I only have one equation and 2 unknown variables so I cannot solve it. How do I proceed from here?