a radio commercial for a loan company states: "You only pay 28 cents a day for each $500 borrowed." If you borrow 2910$ for 151 days.
a) what amount will you repay?
b)what annual interest rate is the company actually charging? (Assume a 360-day year.)
a) To find the total amount to repay, we need to calculate the number of $500 increments in the loan amount and then multiply it by the cost per day.
Number of $500 increments = loan amount / $500 = $2910 / $500 = 5.82 increments
Total cost per day = cost per day per $500 * number of $500 increments = 28 cents * 5.82 = $1.6296
Total amount to repay = total cost per day * number of days = $1.6296 * 151 = $246.27
b) To find the annual interest rate, we need to calculate the interest paid per year and divide it by the loan amount.
Interest paid per year = total amount to repay - loan amount = $246.27 - $2910 = -$2663.73
Annual interest rate = (interest paid per year / loan amount) * 100 = (-$2663.73 / $2910) * 100 = -91.54%
Since the interest rate is negative, it means that the company is actually refunding money to the borrower, which is not a realistic scenario.
To calculate the amount you will repay, we need to calculate the daily cost and then multiply it by the number of days borrowed.
a) Calculate daily cost:
The radio commercial states that you only pay 28 cents a day for each $500 borrowed. So, we can calculate the daily cost for borrowing $500 as:
$500 * 28 cents = $140 per day
Next, divide the borrowed amount by $500 to get the number of $500 increments:
$2910 / $500 = 5.82 (rounded to 2 decimal places)
Finally, multiply the daily cost by the number of $500 increments and the number of days borrowed to get the total amount repaid:
$140 * 5.82 * 151 = $127,459.80
b) Now, let's calculate the annual interest rate by using the formula for simple interest:
Interest = Principal * Rate * Time
Let's assume the annual interest rate is "r."
Using the given information, we can set up the following equation:
$127,459.80 = $2910 * r * (151/360)
Simplifying the equation:
r = ($127,459.80 / $2910) * (360/151)
r ≈ 300.29%
Therefore, the company is actually charging an annual interest rate of approximately 300.29%.
To calculate the amount you will repay and the annual interest rate charged by the loan company, we'll follow these steps:
Step 1: Calculate the number of units in each $500 increment.
Divide $2910 (the amount you borrowed) by $500.
Number of units = 2910 / 500 = 5.82
Step 2: Round up the number of units to the nearest whole number.
Since you can't have a fractional number of units, round up 5.82 to 6.
Step 3: Calculate the total cost for each unit.
Multiply the number of units by the cost per unit stated in the radio commercial.
Cost per unit = $0.28
Total cost for each unit = 6 * $0.28 = $1.68
Step 4: Calculate the total amount you will repay.
Multiply the total cost for each unit by the number of days.
Number of days = 151
Total repayment = $1.68 * 151 = $253.68
Answer to part a): You will repay $253.68.
Step 5: Calculate the annual interest rate.
To find the annual interest rate, we need to consider that the loan term is 151 days in a 360-day year.
Annual interest rate = (Total repayment / Amount borrowed) * (360 / Number of days)
Amount borrowed = $2910
Annual interest rate = ($253.68 / $2910) * (360 / 151)
Answer to part b): The loan company is actually charging an annual interest rate of approximately 48.99%.