Problem
To pay for car repairs, you take out a simple interest loan for $\$ 1480$ at a rate of $6.5 \%$ for 180 days. Answer parts (a) $-(c)$ a. Find the interest you will pay if the lender uses the Banker's Rule ( 360 days in a year). The interest you will pay if the lender uses the Banker's Rule will be $\$ 48.10$. (Do not round until the final answer. Then round to the nearest cent as needed.) b. Find the interest you will pay if the lender uses 365 days in a year. The interest you will pay if you repay the loan after 180 days is $\$$ (Do not round until the final answer. Then round to the nearest cent as needed.)
Solution
Step 1 ：We are given that the principal amount (P) is $1480, the annual interest rate (R) is 6.5% or 0.065 in decimal form, and the time (T) is 180 days. However, we need to convert this time into years. Since the lender uses 365 days in a year, we divide 180 by 365 to get approximately 0.49315 years.
Step 2 ：We can now substitute these values into the formula for simple interest, which is I = PRT.
Step 3 ：Substituting the given values, we get I = 1480 * 0.065 * 0.49315.
Step 4 ：Calculating the above expression, we find that the interest you will pay if the lender uses 365 days in a year is approximately $47.44.
Step 5 ：\(\boxed{47.44}\) is the final answer.
