Let
C----------------- > charges for the purchases to the credit card
r------------------- > the interest rate
X------------------ > total cost of the purchase
we know that
C=4120
r= 22.45%=0.2245
X=C*(1+r)
substituting the values in the formula
X=(4120)*(1+0.2245)= (4120)*(1.2245)=5044.94
the answer is $5044.94