It should just be:

previous period balance * interest rate / 52 = interest charged in current period

When I do that with your numbers, though, I don't get the exact answer they do:

204062.75 * 3.69 / 100 / 52 = $144.81

compared to the $143.14 that they show on line 2.

It could be that the interest rate you're listing (3.69) is the effective APR and not the nominal rate on the loan. It could also be that they do the amortization slightly differently since you have a weekly payment -- I haven't seen that before, and I'm not sure how the bank deals with the fact that a year is typically 52 weeks and 1 day long.

If you don't mind a little inaccuracy, the above formula should work. Your new balance will just be your old balance plus the interest as calculated above minus your payment amount. To get rid of the inaccuracy you'd probably have to ask your bank for more details about exactly how they calculate things.

2Cor521