Company 1 pays A% Interest every T days

Company 2 pays B% Interest (>A%) every T days

Company 1 has an initial investment of $X dollars

Company 2 requires an inital fee of $Y dollars to invest in their company ($Y does not pay any interest! It's a fee.)

At what point T in terms of A, B, X and Y should I stop investing in Company 1 and begin investing in Company 2 to obtain the maximum return at T=infinity? Investments are non-refundable.

Example:

$1,000 invested in A at 3% interest

B pays 8% interest

B requires a $1,000 fee to invest.

By brute force calculation, the optimum T value is approx 16 for this example. ($1604.71 invested in Company 1). This results in the first interest earning investment in B at T=39. (Only slightly later then T=0 with $1000 in company where the first interest earning payment would be made at T=36).