Interest due is proportional to the interest rate, the amount borrowed, and the time period. The daily interest rate is often computed as 1/365 of the annual interest rate. "45 days of accrued interest" means the interest due on the borrowed amount after 45 days.
The applicable formula is
I = Prt
That is, the interest due (accrued) is the product of the principal amount borrowed (P), the annual interest rate (r) and the number of years (t). 45 days will be 45/365 of one year.
45 days of accrued interest is
I = $1455.69 × 0.128 × (45/365) = $22.97
The $250 you pay will go to pay the late charge ($35), the interest due ($22.97) and the remainder will be applied to the principal. The new balance is
$1455.69 + 35.00 + 22.97 - 250.00 = $1263.66
