A radio commercial for a loan company states: "You only pay 34 cents a day for each $500 borrowed." If you borrow 2236$ for 260 days, what amount will you repay, and what annual interest rate is the company actually charging? (Assume a 360-day year.)
To find out the amount you will repay, you need to calculate the daily payment and then multiply it by the number of days you borrowed the money for.
Given that you only pay 34 cents per day for each $500 borrowed, the daily payment per $500 borrowed is $0.34. Since you borrowed $2,236, the amount you borrow can be divided into 500: $2,236 ÷ 500 = 4 remainder 236.
Therefore, the daily payment for $2,236 is the sum of the daily payment for the full $500 and the daily payment for the remainder: $0.34 + $0.34 = $0.68.
Now, let's calculate the number of daily payments over 260 days. Multiply the number of full $500 by 260 days and add the daily payment for the remainder of $236: 4 × 260 = 1,040 and $0.68 × 260 = $176.80.
Next, add the two results together: 1,040 + $176.80 = $1,216.80.
Therefore, the total amount you will repay is $1,216.80.
To find the annual interest rate, divide the total amount repaid by the original amount borrowed, then divide by the number of days in a year:
Interest Rate = (Total Repay / Original Borrowed Amount) / Number of Days in a Year
Interest Rate = ($1,216.80 / $2,236) / 360
Using a calculator, divide $1,216.80 by $2,236 to obtain 0.5443. Then, divide 0.5443 by 360 to get 0.0015119.
To express it as a percentage, multiply by 100: 0.0015119 × 100 = 0.15119.
The loan company is therefore charging an annual interest rate of 0.15119%, or approximately 0.15%.
To calculate the total amount you will repay, we need to determine the number of $500 increments in your loan amount.
2236$ ÷ $500 = 4.472
Since you can't have a fraction of a $500 increment, we need to round up to the nearest whole number. Therefore, you borrowed 5 increments of $500.
Next, we calculate the daily repayment amount for each $500 borrowed.
34 cents × 5 increments = $1.70
To find the total amount repaid over 260 days, multiply the daily repayment amount by the number of days.
$1.70 × 260 days = $442.00
Therefore, you will repay a total of $442.00.
Now, let's calculate the annual interest rate the company is charging.
The interest rate is calculated based on a 360-day year, so we need to convert the daily repayment amount to an annual repayment amount.
$1.70 × 360 days = $612.00
To find the annual interest rate, we divide the total repayment amount by the loan amount and multiply by 100.
($612.00 / $2236.00) × 100 = 27.38%
Therefore, the loan company is actually charging an annual interest rate of 27.38%.
To calculate the amount you will repay and the annual interest rate being charged, we can follow these steps:
Step 1: Calculate the total number of 34 cent payments for each $500 borrowed.
Since the radio commercial states that you only pay 34 cents a day for each $500 borrowed, we can calculate the number of 34 cent payments for $2236 by dividing $2236 by $500 and then multiplying it by 34:
Number of 34 cent payments = (2236 / 500) * 34 = 151.12
However, since we cannot have a fraction of a payment, we need to round this down to the nearest whole number. Therefore, the total number of 34 cent payments is 151.
Step 2: Calculate the total repayment amount.
To find the total repayment amount, we multiply the number of 34 cent payments by $500:
Total repayment amount = 151 * $500 = $75,500
Step 3: Calculate the annual interest rate.
To calculate the annual interest rate, we need to find the rate that corresponds to the total repayment amount over 260 days. We can use the following formula:
Annual interest rate = (Total repayment amount / Loan amount) * (360 / Number of days)
In this case, the Loan amount is $2236 and the Number of days is 260. Plugging in these values:
Annual interest rate = ($75,500 / $2236) * (360 / 260) = 12.76
Therefore, the loan company is charging an annual interest rate of 12.76%.