Math Skill 4 - Credit Cost Calculations

These calculation steps can be used for ANY type of loan where you have fixed payments and fixed interest rates over time. This includes mortgages, car loans, student loans, personal loans, home equity loans, and (most of the time) credit cards. Not every type of problem will necessarily require you to follow every single step, however. If you are feeling uncertain about whether you can skip certain steps or not, just follow them all. If you correctly follow EVERY step in the correct order, you will NEVER get the incorrect answer for any problem in this unit.

Process & formulas:

1) Find Loan Amount = Sales Price – Down Payment

2) Find Payment and N = TVM calculation

3) Find Total Loan Payments = Pmt * N

4) Find Finance Charge = Total Loan Payments – Loan Amount

5) Find Total Cost = Finance Charge + Sales Price

Notice that this process separates the cost of the loan (which we call the “finance charge”) from the cost of the item being purchased. The total cost is the sum of the cost of the loan and the cost of the item.

Example Questions

Example 1

Suppose Jon has $2000 debt on his credit card (20% APR), with a required minimum payment of $35 per month. If Jon pays the minimum each month, how much interest (finance charge) did Jon pay?

Solution:

Let’s go through the calculation steps!

1) Find Loan Amount = Sales Price – Down Payment

$2,000 - $0 = $2,000

2) Find Payment and N = TVM Calculation

Pmt = $35, N = 184.1894

3) Find Total Loan Payments = Pmt * N

35 * 184.1894 = $6,446.63

4) Find Finance Charge = TLP– Loan Amount

$6,446.63 - $2,000 = $4,446.63

Example 2

Jodie just bought a new car. She paid $21,000 for the car and used the $2,500 trade-in value of her old car as a down payment. If her interest rate is 6.5% for 5 years, what is the total cost of buying the car?

Solution:

Let’s go through the calculation steps!

1) Find Loan Amount = Sales Price – Down Payment

$21,000 - $2,500 = $18,500

2) Find Payment and N = TVM Calculation

N = 60, Pmt = $361.97

3) Find Total Loan Payments = Pmt * N

361.97 60 = $21,718

4) Find Finance Charge = TLP– Loan Amount

$21,718 - $18,500 = $3,218

5) Total Cost = Finance Charge + Sales Price

$3,218.42 + $21,000 = $24,218

Watch it in action!

Practice Questions

1. Victoria has a $7,500 balance on her credit card. She just got married and would like to have a baby soon but doesn’t want to do so until her credit card is paid off. If the interest rate on the card is 19% and she can afford a monthly payment of $200, how many years will it take her to pay off the credit card?

2. How much interest will Victoria (from question 1) have paid on her credit card by the time it is paid off?

3. John borrowed $32,000 in student loans to complete his bachelor’s degree. The interest on the loans is 3.4%. If he pays off these loans in 5 years, then how much interest will he have paid?

4. You are with your friend Russell at the car dealership. Russell is looking to buy a car. He told the salesperson that he wanted a payment of $350/month. The dealership has offered to sell him the car he wants for a payment of $350 at 0% for 5 years with a $5,000 down payment. Russell is eager to take the deal because of the 0% interest rate. You wander over to the car and notice that the sticker price is $23,000. Based on this information, would you recommend that Russell take the deal the dealership is offering?

5. Pedro is looking to buy a house. He is going to buy a home for a sales price of $220,000 and has been approved for a loan at 8% for 30 years and will be making a down payment of $40,000. What will the total cost of the house be? (HINT: This question will require you to perform every step of the credit calculation process, including finding the sales price, payment, and finance charge).

6. Vaan made a $25,000 down payment on a $450,000 house. If he paid 11.5% interest per year for 30 years, what was the total cost of the house?

7. Barrett buys a $12,000 car with his credit card. If he makes the minimum payment of $250 per month at a 19% interest rate, how much interest has he paid on the car?

8. Barrett (from previous) has a friend who convinces him it's worth the hassle of getting a proper vehicle loan. He is approved for a 5-year loan at 6.8 % interest. How much interest does he pay for the car using the car loan?

9. Lee is at the car dealership. He has successfully negotiated a sales price of $36,000, with an $8,000 down payment from the trade-in of his old car. The salesman has now offered him a 0% loan for 48 months. Calculate his monthly payment, his total interest, and his total cost of the car.

10. Lee (from previous) had pushes for another financing alternative. The salesman then offers to give him $7,000 in savings on the car (i.e. reduction in sales price), but if he does so he will have to pay 4.5% interest for 60 months. Calculate his monthly payment, his total interest, and his total cost of the car in this scenario. Which deal should he take? The 0%, $0 cash back from #9, or the $7,000 savings at 4.5% interest from #10?

Solutions

1) This is a simple time value of money question because there is no down payment or sales price involved in credit card calculations. In this case, we are being asked to find N. PV = 7,500; FV = 0; I/Y = 19/12; PMT = -200. Computing N gives 57.34. This is the number of MONTHS. Divide by 12 to find the answer is N = 4.78 years.

2) Let’s go through our credit calculation steps. In question 1, we found the loan amount (7,500), the pmt (200), and N (57.34). This means that we are on step 3 of the process. The next step is to calculate the total paid on the loan. We can calculate the total amount paid on the loan by multiplying N*PMT = 57.34*200 = $11,468. Total interest is found by subtracting the principal balance from the total paid. When we subtract the original $7,500 balance from the $11,465 total paid, we find the total interest charged to Victoria is 3,968.

3) Let’s go through our credit calculation steps. First, we need the loan amount. This is easy: it’s just the $32,000 he borrowed. Next, we need PMT and N. N is given as 5 years, but we don’t know the PMT, so we will have to calculate it. PV = 32,000; FV = 0; N = 5*12, I/Y = 3.4/12 CPT PMT = 580.70. Now that we know PMT and N, we can calculate the total paid = PMT * N = 580.70*60 = $34,842. Since each payment is composed of only principal and interest, we can subtract the principal from the total paid to get the interest cost. Total Paid – Principal = 34,842 – 32,000 = $2,842. This is the total interest paid, and the answer to the question.

4) What this question is really asking you to do is calculate the sales price of the car based upon the loan information. Since Loan Amount = Sales Price – Down Payment, then the Sales Price = Loan Amount + Down Payment (who ever said you wouldn’t use algebra in real life? J ). We know the down payment is $5,000, so all we need now is the loan amount. A simple TVM calculation (FV = 0; I/Y = 0; N = 5*12; PMT = -350) will tell you that the PV = $21,000. If we add the $5,000 down payment to the loan amount of $21,000, we find that the sales price of the car is $26,000. Since this is well over the sticker price, Russell is getting cheated, and he most certainly should not take the financing deal! NOTE: this is a little harder than most questions because it requires you to use critical thinking about the math process - you can’t just follow our steps. If you struggle on this question, it may help if you think of it as a simple TVM problem (which you mastered in unit 1), with a down payment added.

5) This one seems hard only because it requires you to follow through every step of the credit calculation process. Let’s start at the top. The loan amount is the sales price – down payment = 220,000 – 40,000 = $180,000. Next, we need PMT and N. N is given, but PMT has to be calculated using TVM. PV = 180,000; FV = 0; N = 30*12; I/Y = 8/12 CPT PMT = $1,320.78. Next step is to find total paid = PMT * N = $1,320.78 * 360 = $475,479. Next step is to find finance charge = Total Paid – Loan Amount = 475,479 – 180,000 = $295,479 in interest. Now we can find the total cost of the home by adding the finance charge to the sales price. Total cost = $220,000 + $295,479 = $515,479.

6) Loan amount = $450,000 – $25,000 = $425,000

Solve for PMT = $4,208.74

T.L.P. = $4,208 * 360 = $1,515,146

Finance Charge = $1,515,146-$425,000 = $1,090,146

Total Cost = $1,090,146 + $450,000 = $1,540,146

7) Loan amount = $12,000 – $0 = $12,000

Solve for N = 90.84

T.L.P. = $250 * 90.84 = $22,711

Finance Charge = $22,711-$12,000 = $10,711

8) Loan amount = $12,000 – $0 = $12,000

Solve for PMT = $236.48

T.L.P. = $236.48311.2866* 60 = $14,188

Finance Charge = $14,188 - $12,000 = $2,188

9) Loan Amount = $36,000 - $8,000 = $28,000

Solve for PMT = $583.33

T.L.P. = $583 * 48 = $28,000

Finance Charge = $28,000 - $28,000 = $0 (think a moment about why this is the case!)

Total cost = $36,000 + $0 = $36,000

10) Sales Price = $36,000 - $7,000 = $29,000

Loan Amount = $29,000 - $8,000 = $21,000

Solve for PMT = $391.50

T.L.P. = $391.50 * 60 = $23,490

Finance Charge = $23,490 - $21,000 = $2,490

Total Cost = $29,000 + $2,490 = $31,490

Remember that the rebate reduces the sales price. Therefore, the sales price is only $29,000 if he takes the rebate. In other words, the $29,000 is the price AFTER the $7,000 rebate. We have to take it off the sales price at the beginning of the problem instead of just subtracting it at the end because the rebate saves him not only the $7,000, but also the interest he would have paid on the $7,000 that he would have had to borrow if not for the rebate. So we take our lower sales price, subtract his down payment to get his loan amount, and then run the rest of our calculations. NOTE: It’s cheaper to pay the interest because he pays LESS in interest than he saves from the cash rebate being offered!