Credit Card Payments

QUESTION

1 A credit card holder has an outstanding balance on four different credit cards. Which method of paying off the credit card will save the most money?

A Snowballing payments according to the highest interest rate

B Snowballing payments according to the lowest balance

C Making fixed payments each month

D Paying the minimum balance each month

2 A bank offers three mortgages shown:

Option 1: Balloon mortgage at 5% with terms 30/5

Option 2: Fixed rate mortgage at 3% for 30 years

Option 3: Adjustable rate mortgage at 4% for 15 years with terms 3/1 and a cap of 2/8

Which mortgage(s) will have fixed payments for at least the first 4 years?

A  Fixed rate only

B  Fixed rate and balloon only

C Fixed rate and adjustable rate only

D Fixed rate, adjustable rate, and balloon

3 Review the information given based on a principal balance of $8,000 to answer the question:

FICO Score	Simple Interest Rate	Total # of Payments	Total Amount Paid
800-850	12%	29	$9,256.00
740-799	15%	33	$9,812.00
670-739	18%	38	$10,554.00
580-669	21%	48	$11,891.00
300-579	28%	60	$14,945.00

 

Calculate how much more a household with a credit score of 525 will pay compared to a household with a credit score of 675.

A $4,391

B $1,337

C $2,604

D $3,491

4 A video streaming service subscriber pays $99.99 per year for unlimited streaming. The subscriber pays for the service using a credit card with a 23.99% APR. The subscriber makes a payment of $15 for three months and then pays the balance off at the end of the fourth month. Determine how much additional interest the subscriber paid by paying the balance off in four months instead paying it off during the grace period.

A $7.67

B $2.56

C $6.41

D $1.15

5 A student is graduating from college in six months but will need a loan in the amount of $2,560 for the last semester. The student receives a PLUS Loan with an interest rate of 7.8%, compounded monthly. What is the balance of the PLUS loan at the time of graduation?

A $2,560.00

B $2,739.61

C $2,648.28

D $2,661.48

6 A consumer owes $2,550 on a credit card with a 21.9% annual interest rate.

Assuming the consumer makes fixed payments and does not charge any more purchases with the card, what is the total monthly payment needed to pay off the card in three years? Show all work and round your answer to the nearest penny.

 

7 A new homeowner bought a refrigerator from a discount appliance store. After making a $200 down payment, the remaining balance was financed using an installment loan. The homeowner makes 12 equal credit card payments of $59.81 to pay off the loan. The discount appliance store charges $1.50 for every payment made by credit card. The homeowner also had to pay late fees in the amount of $25 three different times.

 

What is the total cost of the refrigerator? Show all necessary work.

Part 2

 

1 A college student plans to use a credit card to cover the cost of purchasing a $3,200 campus meal plan. If the credit card has annual interest rate of 12.99% compounded continuously and the student plans to pay off the loan in 20 months, how much interest will be owed?

A $773.51

B $816.76

C $842.93

D $949.35

2 To pay for a home improvement project that totals $20,000, a homeowner is choosing between two different credit card loans with an interest rate of 6%. The first credit card compounds interest semi-annually, while the second credit card compounds quarterly. The homeowner plans to pay off the loan in 10 years.

 

Part A: Determine the total value of the loan with the semi-annually compounded interest. Show all work and round your answer to the nearest hundredth. (4 points)

 

Part B: Determine the total value of the loan with the quarterly compounded interest. Show all work and round your answer to the nearest hundredth. (4 points)

 

Part C: What is the difference between the total interest accrued on each loan? Explain your answer in complete sentences. (2 points)

 

3 A small business owner is applying for a small business loan and has been approved for a $50,000 loan with 4.35% annual interest. The first loan is a simple interest rate, the second loan compounds interest quarterly, and the third loan compounds interest continuously. The small business owner plans to pay off the loan in 3 years and 4 months.

 

Part A: Determine the total value of the loan with the simple interest. Show all work and round your answer to the nearest hundredth. (3 points)

 

Part B: Determine the total value of the loan with the quarterly compounded interest. Show all work and round your answer to the nearest hundredth. (3 points)

 

Part C: Determine the total value of the loan with the continuously compounded interest. Show all work and round your answer to the nearest hundredth. (2 points)

Part D: Using the values from Parts A, B, and C, explain which loan option is the best choice for the small business owner. (2 points)

ANSWER

Credit Card Payments

The method that will save the most money is A. Snowballing payments according to the highest interest rate. This strategy involves paying off the credit card with the highest interest rate first, which minimizes the overall interest paid.

Mortgages with Fixed Payments

The mortgage(s) with fixed payments for at least the first 4 years are:

B. Fixed rate and balloon only: The fixed-rate mortgage will have consistent payments over the entire term, and the balloon mortgage will have fixed payments for the initial 5 years.

Credit Score and Interest Costs:

To calculate the difference in interest costs between a credit score of 525 and 675, we can subtract the total amount paid for each score.

For a score of 525:

• Total Amount Paid = $14,945.00

For a score of 675:

• Total Amount Paid = $10,554.00

The difference is $14,945.00 – $10,554.00 = $4,391. So, the answer is A. $4,391.

Interest on Streaming Service Subscription:

To calculate the additional interest paid by paying off the balance in four months instead of during the grace period, we need to find the interest for four months on the remaining balance.

The annual interest rate is 23.99%, so the monthly rate is 23.99% / 12 = 1.9992%.

Interest for four months = $99.99 * 1.9992% * 4 = $7.99.

Since the subscriber paid $15 for three months, we subtract that from the interest: $7.99 – $15 = -$7.01 (negative because they overpaid).

So, the additional interest paid is $7.01.

Balance of PLUS Loan:

To find the balance of the PLUS loan at graduation, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where: A = Future balance P = Initial principal ($2,560) r = Annual interest rate (7.8% or 0.078) n = Number of times interest is compounded per year (monthly, so 12) t = Number of years (6 months or 0.5 years)

A = $2,560(1 + 0.078/12)^(12*0.5) A ≈ $2,739.61

So, the balance of the PLUS loan at graduation is approximately $2,739.61.

Paying Off Credit Card Debt:

To calculate the total monthly payment needed to pay off the credit card in three years, we can use the formula for monthly payments on a loan:

M = [P * (r / 12)] / [1 – (1 + r / 12)^(-nt)]

Where: M = Monthly payment P = Principal balance ($2,550) r = Annual interest rate (21.9% or 0.219) n = Number of times interest is compounded per year (assuming monthly, so 12) t = Number of years (3)

M = [$2,550 * (0.219 / 12)] / [1 – (1 + 0.219 / 12)^(-12*3)] M ≈ $104.42

So, the total monthly payment needed to pay off the card in three years is approximately $104.42.

Total Cost of Refrigerator:

To calculate the total cost of the refrigerator, we need to consider the following components:

Initial down payment: $200

12 credit card payments: $59.81 each

Credit card payment fees: $1.50 for each of the 12 payments

Late fees: $25 x 3

Total Cost = $200 + (12 * $59.81) + (12 * $1.50) + (3 * $25) = $1,042.92.

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Credit Card Loan for Meal Plan

To calculate the interest owed on the credit card loan for the campus meal plan, we can use the continuous compounding formula:

A = P * e^(rt)

Where: A = Future balance (including interest) P = Principal amount ($3,200) r = Annual interest rate (12.99% or 0.1299) t = Time in years (20 months / 12 months per year)

A = $3,200 * e^(0.1299 * (20/12)) A ≈ $3,973.27

The interest owed is the difference between the future balance and the principal amount: $3,973.27 – $3,200 = $773.27.

Home Improvement Project Loans

Part A: Semi-annually compounded interest:

A = P * (1 + (r/n))^(nt) A = $20,000 * (1 + (0.06/2))^(2*10) A ≈ $32,509.67

Part B: Quarterly compounded interest:

A = P * (1 + (r/n))^(nt) A = $20,000 * (1 + (0.06/4))^(4*10) A ≈ $33,156.04

Part C: Difference in total interest:

The difference in total interest between the two loans is the result from Part B minus the result from Part A: $33,156.04 – $32,509.67 ≈ $646.37.

Small Business Loan Options:

Part A: Simple interest:

A = P * (1 + rt) A = $50,000 * (1 + 0.0435 * 3.33) A ≈ $56,625

Part B: Quarterly compounded interest:

A = P * (1 + (r/n))^(nt) A = $50,000 * (1 + (0.0435/4))^(4*3.33) A ≈ $57,438.39

Part C: Continuously compounded interest:

A = P * e^(rt) A = $50,000 * e^(0.0435 * 3.33) A ≈ $57,016.39

Part D: The best loan option for the small business owner would be the simple interest loan (Part A) as it results in the lowest total cost over the given time frame. This is because it does not involve compounding, which reduces the overall interest paid.