Questions: Joe obtains a loan for home renovations from a bank that charges simple interest at an annual rate of 16%. His loan is for 14,500 for 61 days. Assume each day is 1/365 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 61 days. (b) Assuming Joe doesn't make any payments, find the amount owed after 61 days.

Solution Steps

We are given the following information:

• Principal amount (\(P\)) = \$14,500
• Annual interest rate (\(r\)) = 16\% = 0.16
• Time period (\(t\)) = 61 days

Since the interest is simple interest, we use the formula for simple interest: \[ I = P \times r \times t \]

The time period is given in days, and we need to convert it to years. Since each day is \(\frac{1}{365}\) of a year, we have: \[ t = \frac{61}{365} \]

Substitute the values into the simple interest formula: \[ I = 14500 \times 0.16 \times \frac{61}{365} \]

Calculate the interest: \[ I = 14500 \times 0.16 \times 0.1671 \approx 388.49 \]

The total amount owed after 61 days is the sum of the principal and the interest: \[ A = P + I = 14500 + 388.49 = 14888.49 \]

Final Answer