1. Your average daily balance on your charge card for the month of July is $855.28. If your card carries an annual interest rate of 15.4%, what will your finance charge be for July?
2. You buy a car from your neighbor at a price of $9,000. You pay $500 down and pay 9.5% on the balance. If you make monthly payments of $200, how many months (to the nearest hundredth of a month) will it take to pay off the loan?
3. You get a $15,000 car loan for 4 years at 6.75% interest. The lender charges $250 for an origination fee (which is added to your loan amount). What is your APR?
4. Todd buys a car for $18,000. He must also pay tax and license fees of $1,200. He borrows $17,000 for 4 years at 7.25% interest, with monthly payments. What is the total cost of the car, to the nearest dollar?
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1. To calculate the finance charge for July, we need to know the daily periodic rate, which can be calculated by dividing the annual interest rate by the number of days in a year (365). Therefore, the daily periodic rate would be 15.4% / 365 = 0.00042.
Next, we need to calculate the average daily balance, which is $855.28. Multiply this by the number of days in July to get the total balance: $855.28 * 31 = $26,531.68.
Now, multiply the total balance by the daily periodic rate to get the finance charge: $26,531.68 * 0.00042 = $11.13.
Therefore, the finance charge for July would be $11.13.
2. To calculate the number of months it will take to pay off the loan, we need to consider both the down payment and the interest rate.
First, subtract the down payment from the total price of the car: $9,000 - $500 = $8,500.
Next, determine the monthly interest rate by dividing the annual interest rate by 12: 9.5% / 12 = 0.00792.
Now, we need to calculate the number of months it will take to fully pay off the loan. We can use a loan amortization formula to find the answer:
n = -log(1 - (r * p) / A) / log(1 + r)
Where:
n = the number of months
r = the monthly interest rate
p = the monthly payment
A = the remaining balance
In this case, r = 0.00792, p = $200, and A = $8,500.
Plugging in the values, the formula becomes:
n = -log(1 - (0.00792 * 200) / 8500) / log(1 + 0.00792)
Using a calculator, we find n ≈ 49.49 months.
Therefore, it will take approximately 49.49 months (or rounded to the nearest hundredth - 49.50 months) to pay off the loan.
3. To find the APR (Annual Percentage Rate), we need to consider the interest rate and any additional fees that are included in the loan.
In this case, the loan amount is $15,000 and there is an origination fee of $250, which is added to the loan amount. Therefore, the total loan amount is $15,000 + $250 = $15,250.
Now, let's calculate the interest paid over the 4-year term. We can use the formula: Interest = Principal * Interest Rate * Time.
Interest = $15,250 * 6.75% * 4 = $4,335.
Next, let's calculate the average outstanding balance, which is half the loan amount: $15,250 / 2 = $7,625.
Now, let's calculate the APR using the following formula:
APR = (Interest / Average Outstanding Balance) * 100.
APR = ($4,335 / $7,625) * 100 ≈ 56.77%.
Therefore, the APR for this car loan is approximately 56.77%.
4. To calculate the total cost of the car, we need to consider the purchase price, tax and license fees, and the interest paid over the loan term.
The purchase price of the car is $18,000, and the tax and license fees are $1,200. So the total cost of the car without considering interest is $18,000 + $1,200 = $19,200.
Next, let's calculate the interest paid over the 4-year loan term. We can use the formula: Interest = Principal * Interest Rate * Time.
Interest = $17,000 * 7.25% * 4 = $4,660.
Now, let's calculate the total cost of the car by adding the purchase price, tax and license fees, and the interest paid: $19,200 + $4,660 = $23,860.
Therefore, the total cost of the car, rounded to the nearest dollar, is $23,860.