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, what amount will you repay?
what annual interest rate is the company actually charging? (Assume a 360-day year.)
To determine the amount to be repaid, we need to calculate the total number of cents borrowed and multiply it by 28. The total number of $500 increments borrowed would be 2910 / 500 = 5.82 increments. To round this up to the nearest whole number, we can assume 6 increments were borrowed.
Thus, the total number of cents borrowed would be 6 increments * $500/increment * 100 cents/dollar = 30000 cents.
Multiplying this by the cost per day, we get the amount to be repaid: 30000 cents * $0.28/cent = $8400.
To calculate the annual interest rate, we can use the formula for simple interest:
Interest = Principal * Rate * Time
Rearranging the formula, we have:
Rate = Interest / (Principal * Time)
We can plug in the values: Principal = $2910, Interest = $8400 - $2910 = $5490, and Time = 151 days / 360 days/year.
Rate = $5490 / ($2910 * (151/360)) = 0.47 or 47%.
Therefore, the loan company is actually charging an annual interest rate of 47%.
To determine the amount you will repay, you need to calculate the total cost based on the given information.
Step 1: Calculate the number of $500 increments in your total borrowed amount:
$2910 ÷ $500 = 5.82 (rounded to the nearest whole number) or 6
Step 2: Calculate the cost per day for each $500 borrowed:
28 cents × 6 (number of $500 increments) = $1.68
Step 3: Calculate the total cost for 151 days:
$1.68 × 151 = $253.68
Therefore, you will repay $253.68.
To determine the annual interest rate, you need to find the rate that corresponds to the cost of borrowing for 151 days.
Step 4: Calculate the interest rate per day:
$1.68 ÷ $500 = 0.00336
Step 5: Calculate the annual interest rate:
0.00336 × 360 = 1.2096
Therefore, the loan company is actually charging an annual interest rate of approximately 120.96%.
To find out the amount you will repay, you need to calculate the total cost of borrowing and add it to the amount borrowed.
1. Calculate the daily cost of borrowing per $500: Since the radio commercial states that you pay 28 cents a day for each $500 borrowed, divide 0.28 by 500:
Daily cost per $500 = 0.28 / 500 = 0.00056 dollars per day per $500.
2. Calculate the total days for which you borrowed: You borrowed the money for 151 days.
3. Calculate the number of $500 units in the borrowed amount: Divide the loan amount by $500:
Number of $500 units = 2910 / 500 = 5.82 units (rounded to two decimal places).
4. Calculate the total cost of borrowing for the loan amount:
Total cost of borrowing = Daily cost per $500 * Number of $500 units * Total days borrowed
= 0.00056 * 5.82 * 151
Now, to find the total amount you will repay, add the loan amount to the total cost of borrowing:
Total repayment amount = Loan amount + Total cost of borrowing.
To calculate the annual interest rate, you'll need to use the formula for annual percentage rate (APR):
APR = (Total cost of borrowing / Loan amount) * (360 / Total days borrowed)
Substituting the values calculated from the earlier steps:
APR = (Total cost of borrowing / Loan amount) * (360 / 151)
Now let's plug in the numbers and calculate the results.