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.)

Answer 1

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%.