Questions: A restaurant borrows 19,700 from a local bank for 4 months. The local bank charges simple interest at an annual rate of 2.45% for this loan. 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 the restaurant doesn't make any payments, find the amount owed after 4 months.

A restaurant borrows 19,700 from a local bank for 4 months. The local bank charges simple interest at an annual rate of 2.45% for this loan. 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 the restaurant doesn't make any payments, find the amount owed after 4 months.

Transcript text: A restaurant borrows $\$ 19,700$ from a local bank for 4 months. The local bank charges simple interest at an annual rate of $2.45 \%$ for this loan. 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 4 months. $\$ \square$ (b) Assuming the restaurhnt doesn't make any payments, find the amount owed after 4 months. $\$ \square$

Solution

Solution Steps

Step 1: Convert the annual interest rate from a percentage to a decimal

To convert the annual interest rate from a percentage to a decimal, we divide the rate by 100. Thus, $r = \frac{2.45}{100} = 0.0245$.

Step 2: Convert the time from months to years

Given the time in months is 4, we convert this to years by dividing by 12. Therefore, $t = \frac{4}{12} = 0.333$ years.

Step 3: Calculate the simple interest

Using the formula $I = P \times r \times t$, we substitute $P = 19700$, $r = 0.0245$, and $t = 0.333$ to get $I = 19700 \times 0.0245 \times 0.333 = 160.88$.

Step 4: Calculate the total amount owed

The total amount owed is calculated by adding the interest to the principal, $A = P + I$. Substituting the values, we get $A = 19700 + 160.88 = 19860.88$.