An accountant for a corporation forgot to pay the firm's...

An accountant for a corporation forgot to pay the firm's income tax of $\$ 321,812.85$ on time. The government charged a penalty based on an annual interest rate of 13.4$\%$ for the 29 days the money was late. Find the total amount (tax and penalty) that was paid. (Use a 365 -day year.)

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Key Concepts

Simple Interest Calculation

This concept involves the calculation of interest on a principal amount over a period of time using a fixed rate. It is determined by multiplying the principal by the rate and the time period (expressed as a fraction of a year), which provides the basis for understanding how additional costs accrue when payments are delayed.

Annual Interest Rate

An annual interest rate represents the percentage of the principal charged or earned over one year. When calculating interest for periods shorter than a year, the annual rate is adjusted by dividing the time period by the number of days in a year, making it essential for understanding late fees, penalties, or returns on investments.

Time Conversion for Interest Calculations

This concept entails converting a specified period, such as days, into a fraction of a year to accurately apply an annual interest rate. It is fundamental when dealing with time-sensitive financial calculations where the period does not span an entire year.