Questions: Heather takes out a loan for her college tuition from a bank that charges simple interest at an annual rate of 16%. Her loan is for 4700 for 10 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 10 months. (b) Assuming Heather doesn't make any payments, find the amount owed after 10 months.

Heather takes out a loan for her college tuition from a bank that charges simple interest at an annual rate of 16%. Her loan is for 4700 for 10 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 10 months. (b) Assuming Heather doesn't make any payments, find the amount owed after 10 months.

Transcript text: Heather takes out a loan for her college tuition from a bank that charges simple interest at an annual rate of $16 \%$. Her loan is for $\$ 4700$ for 10 months. Assume each month is $\frac{1}{12}$ 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 10 months. $\$$ $\square$ (b) Assuming Heather doesn't make any payments, find the amount owed after 10 months. $\$$ $\square$

Solution

Solution Steps

Step 1: Identify the given values

Principal amount ($ P $) = \$4700
Annual interest rate ($ r $) = 16% = 0.16
Time ($ t $) = 10 months = $ \frac{10}{12} $ years

Step 2: Calculate the simple interest

The formula for simple interest is: \[ I = P \cdot r \cdot t \] Substitute the given values: \[ I = 4700 \cdot 0.16 \cdot \frac{10}{12} \] \[ I = 4700 \cdot 0.16 \cdot 0.8333 \] \[ I = 626.6667 \]

Step 3: Calculate the total amount owed

The total amount owed ($ A $) is the sum of the principal and the interest: \[ A = P + I \] \[ A = 4700 + 626.6667 \] \[ A = 5326.6667 \]

Step 4: Round the final answers to the nearest cent