An accountant for a corporation forgot to pay the firm's income tax of $\$ 725,604.83$ on time. The government charged a penalty of $7.9 \%$ interest for the 43 days the money was late. Find the total amount (tax and penalty) that was paid. Assume 365 days in a year.
The total amount paid was $\$ \square$.
(Round to the nearest cent as needed.)
Answer
Final Answer: The total amount paid was \(\boxed{\$732,357.92}\).
Step 1 ：Let's denote the original tax as \(T\), the interest rate as \(r\), the number of days late as \(d\), and the total number of days in a year as \(D\). Given that \(T = \$725,604.83\), \(r = 7.9\% = 0.079\), \(d = 43\) days, and \(D = 365\) days.
Step 2 ：The penalty is calculated as the product of the original tax, the interest rate, and the proportion of the year that the payment was late. The proportion of the year is calculated as the number of days late divided by the total number of days in a year. So, the penalty \(P\) can be calculated as \(P = T \cdot r \cdot \frac{d}{D}\).
Step 3 ：Substituting the given values into the formula, we get \(P = \$725,604.83 \cdot 0.079 \cdot \frac{43}{365} = \$6753.09\).
Step 4 ：The total amount paid is the sum of the original tax and the penalty. So, the total amount paid \(A\) can be calculated as \(A = T + P\).
Step 5 ：Substituting the given values into the formula, we get \(A = \$725,604.83 + \$6753.09 = \$732,357.92\).
Step 6 ：Final Answer: The total amount paid was \(\boxed{\$732,357.92}\).
