I have a solution, but I don't know if the formula is acceptable.
You could use the follow formulas:
I = P x R x T
where I = Interest, P = Principal, R = Rate (%) and T = Term (years)
If Term is to be
a. monthly then, T would be 12 and the R would be R/12
b. weekly then, T would be 52 and the R would be R/52
c. bi-weekly then, T would be 26 and the R would be R/26
with appropriate adjustments to the initial formula.
Typically for simple interest, the amount owed at the end of the term is P + I. Simple.
Your payments, say for a monthly installment, could be calculated as
P = Payment Amount * Term to give the final Principal
Calculate the Interest and SUBTRACT from the Principal.
The interest would be based on the amount agreed to be paid back (payment * term),
but that would NOT be the actual amount generated by the formula before the interest was subtracted.
It would be close for non-extravagant Principals, but would deviate more as the payments increased.
The actual interest rate would not be 5% (for example) but slightly more as in an APR.
If you can provide a better formula for the calculations, the actual calculations would be more accurate.
If you cannot provide a formula for us to use that is acceptable to you, then we are done here.
If the above assumptions are acceptable, then at least attempt a solution for us to discuss.