Questions: John forgot to pay his 394.00 income tax on time. The IRS charged a penalty of 10% simple interest for the 37 days the money was late. Find the penalty that was paid. (Use a 365 day year.) 1.19 3.99 3.89 397.99

John forgot to pay his 394.00 income tax on time. The IRS charged a penalty of 10% simple interest for the 37 days the money was late.

Find the penalty that was paid. (Use a 365 day year.)
1.19
3.99
3.89
397.99

Transcript text: John forgot to pay his $\$ 394.00$ income tax on time. The IRS charged a penalty of $10 \%$ simple interest for the 37 days the money was late. Find the penalty that was paid. (Use a 365 day year.) $\$ 1.19$ $\$ 3.99$ $\$ 3.89$ $\$ 397.99$

Solution

Solution Steps

To find the penalty, we use the formula for simple interest: $ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} $. Here, the principal is \$394.00, the rate is 10% per year, and the time is 37 days out of 365 days in a year.

Step 1: Identify the Given Values

The principal amount is $ \$394.00 $. The annual interest rate is $ 10\% $ or $ 0.10 $. The time period is 37 days, which is $\frac{37}{365}$ of a year.

Step 2: Apply the Simple Interest Formula

The formula for simple interest is: \[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \] Substituting the given values: \[ \text{Interest} = 394.00 \times 0.10 \times \frac{37}{365} \]

Step 3: Calculate the Penalty

Perform the calculation: \[ \text{Interest} = 394.00 \times 0.10 \times 0.1014 \approx 3.994 \]