Questions: Rita takes out a loan for her college tuition from a bank that charges simple interest at an annual rate of 5%, her loan is for 7700 for 4 months. Assume each month is 1/12 of a year. Answer each part below. Do not round any intermediate computations, and round your final answers to the nearest cent. If necessary, refer to the list of financial formulas. (a) Find the interest that will be owed after 4 months. (b) Assuming Rita doesn't make any payments, find the amount owed after 4 months.

Solution Steps

To solve the problem, we need to calculate the simple interest and the total amount owed after 4 months. Simple interest can be calculated using the formula:

\[ \text{Interest} = P \times r \times t \]

where \( P \) is the principal amount, \( r \) is the annual interest rate, and \( t \) is the time in years. After finding the interest, the total amount owed is the sum of the principal and the interest.

To calculate the interest, we first need to convert the time from months to years. Given that the time is 4 months, we convert it as follows:

\[ t = \frac{4}{12} = 0.3333 \text{ years} \]

Using the simple interest formula:

\[ \text{Interest} = P \times r \times t \]

where \( P = 7700 \), \( r = 5.35\% = 0.0535 \), and \( t = 0.3333 \), we calculate:

\[ \text{Interest} = 7700 \times 0.0535 \times 0.3333 = 13731.67 \]

The total amount owed after 4 months is the sum of the principal and the interest:

\[ \text{Total Amount Owed} = P + \text{Interest} = 7700 + 13731.67 = 21431.67 \]

Final Answer