Section 4.6: Installment Buying
- Page ID
- 216985
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- Find amount financed, total installment price, and finance charge for a fixed installment loan.
Now that we’ve spent time studying annuities, you’ve seen how powerful it can be when you make regular payments into an account and let interest work for you. In every annuity example, whether it was saving for retirement, a vacation, a car, or a college fund, we assumed you had time on your side. Time to contribute. Time to grow. Time to wait. But in real life, there are many situations where people don’t have that luxury. Sometimes, you need the money now, not years from now. This is where we naturally transition from annuities to installment loans.
There are two main types of installment loans commonly used: fixed installment loans and amortized loans. A fixed installment loan uses what’s called precomputed interest. With this method, the lender calculates all of the interest up front, usually using simple interest, then adds that interest to the amount financed. The total is then divided by the number of months in the loan term, which creates a set of equal monthly payments. The major disadvantage of a fixed installment loan is that you pay the full amount of precomputed interest even if you pay the loan off early. In other words, making extra payments or paying off the balance ahead of schedule does not save you any interest. You end up paying the same total cost as if you had taken the entire loan term to repay it. Fixed installment loans include personal loans, appliance loans, furniture loans, and some types of consolidation loans.
In contrast, amortized loans are the type used for most car loans, student loans, and mortgages where the interest is calculated very differently. Instead of computing all the interest upfront, an amortized loan calculates interest month by month based on the remaining balance. Because each payment reduces the principal, the amount of interest charged gradually decreases over time, and more of each payment goes toward the principal as the loan progresses. This structure gives borrowers a major advantage over precomputed-interest loans where paying the loan off early saves money. Since interest is only charged on the outstanding balance, making extra payments, whether occasionally or regularly, reduces the principal faster, which in turn reduces the total interest paid over the life of the loan. This makes amortized loans far more consumer‑friendly, especially for people who plan to pay extra or hope to pay off their loan ahead of schedule. We will focus more on amortization loans later in this chapter in Section 4.9.
Why and When to Use Fixed Installment Loans?
An annuity is great when you’re planning ahead. For example:
- You want a new car in five years.
- You want a down payment in ten years.
- You want retirement savings in forty years.
But suppose your car breaks down today, and you need transportation immediately. You may not have five years to save up for a replacement.
Or maybe:
- Your refrigerator stops working this weekend
- Your laptop for school fails mid‑semester
- You need an emergency medical procedure
- You’re offered your dream job, but you must relocate within a month
These are all situations where you can’t wait for money to accumulate through monthly deposits and growth. Life doesn’t schedule emergencies. So instead of saving first and buying later, you often have to buy now and pay over time. That is exactly what a fixed installment loan allows you to do.
Every fixed installment loan includes three key financial ideas:
- Amount Financed
- Total Installment Price
- Finance Charge
Understanding these helps borrowers evaluate whether a loan is affordable and whether it is a good financial decision.
The amount financed is the actual amount of money you borrow from the lender. It is the portion of the loan that represents the “principal”, which is the money being used to purchase the item. The amount financed may include the cash price of the item, minus any down payment, and/or minus any trade-in,
plus certain allowable fees (like taxes or document fees, depending on the lender).
The formula for amount financed is:
Amount Financed = Cash Price − Down Payment
The total installment price is the total amount you will pay over the entire life of the loan, including both:
- the amount financed (principal), and
- the finance charge (the cost of borrowing money)
The formula for the total installment price is:
Total Installment Price = Amount Financed + Finance Charge
This value tells you the true cost of the loan.
The finance charge is the cost of borrowing money. It is the difference between:
- what you actually borrowed, and
- what you end up paying back in total
The formulas for the finance charge:
Finance Charge = \(I=P\cdot r\cdot t\)
Finance Charge = Total Installment Price − Amount Financed
Many people pay attention only to the monthly payment and overlook the total amount they will end up paying. This is especially true with cell phone purchases that have 0% financing. The finance charge reveals the real cost of borrowing and helps consumers compare loans more effectively. The amount financed is the portion of the purchase you actually borrow. It is the number the lender uses to calculate interest. Borrowers often confuse this with the total cost of the loan, but the amount financed is only the size of the loan itself, not the full amount you will pay back. The total installment price, on the other hand, shows the true cost of the loan. It answers the question: “How much money will I spend in total by the time the loan is fully paid off?” Students are often surprised to see how much larger the total installment price is compared to the original amount borrowed. The difference between those two numbers is the finance charge. The finance charge represents the cost of borrowing money. It includes interest, administrative fees, lender risk, and other loan‑related expenses. Essentially, it is the lender’s profit and the borrower’s cost for not paying the full price upfront. This is why it is so important to pay attention to interest rates. For example, many department stores, such as Kohl’s, offer their own store credit cards and advertise deals like “30% off today’s purchase when you use our card.” These promotions often hide extremely high interest rates. Over the past decade, the annual percentage rate (APR) on a Kohl's charge card has typically ranged from 29% to 34%, far higher than the interest rates we usually use in classroom examples. Notice the contrast: In our earlier annuity problems, interest rates ranged from 0.01% to around 9%. But in real life, when you borrow money, the interest rates are usually much higher, and when you invest, the interest rates are usually much lower. Understanding this difference is key to making smart financial decisions.
Store charge cards, also known as closed‑loop retail cards, typically have much higher interest rates than general open-loop credit cards (i.e., Visa, Mastercard, Discover). Closed-loop means that the card can only be used at that retailer. Here are some current rates for some popular cards as of March 2026:
- Kohl’s Credit Card; APR: 30.74%
- Target Red Card; APR: around 25–30%
- Macy’s Store Card; APR: mid-to-high 20% range; Macy’s appears among top retail cards
- Best Buy Store Card; APR: high 20s
- Amazon Store Card; APR: 18.74%–27.49% (variable) for the Prime Visa (open-loop)
- Costco Anywhere Visa: APR: 18.99%–27.74% (variable) (open-loop)
- Ulta Beauty Rewards Card: APR: mid-high 20% range
- Kroger Rewards Mastercard: APR: varies between 25%–30%
Visa, Mastercard, and Discover do not set their own interest rates. The card issuers (banks like Chase, Citi, Discover, Capital One, etc.) set the APR, not the networks.
Credit card networks (Visa, Mastercard, Discover) do not issue most cards and do not control APRs, except Discover and American Express when acting as both network and issuer. However, we can report the typical APR ranges for cards issued on each network, based on aggregated data about major credit card issuers. These ranges represent what typical consumer credit cards carry on each network, based on card issuer data.
- Visa Credit Cards - Issued by banks such as Chase, Bank of America, Citi, Wells Fargo, etc. Based on nationwide averages, Visa cards usually fall in the range of 15% to 24% APR depending on credit quality.
- Mastercard Credit Cards - Issued by banks such as Citi, Capital One, Bank of America, etc. Based on nationwide averages, Mastercard cards fall in the range of 16% to 26% depending on credit quality. Capital One Mastercard often has higher low-end APRs, around 22.94%, one of the highest among issuers. (This is due to the amount of advertising on television networks).
- Discover Credit Cards - Discover is both a network and the issuer, so its interest rates are directly published. Discover has the lowest average APR range among major issuers at 13.85% – 22.70% APR (among the best in the industry). This means Discover cards tend to offer lower rates, especially for customers with good credit.
Jamal has decided to purchase a 3-piece set bedroom set that includes a queen bed frame with storage and two nightstands that costs $1,048.98. He will finance through the retailer's financial services at a rate of 21.99%. He will put a down payment of $200 and finance for 6 months.
- Find the amount financed.
- Find the finance charge.
- Find the total installment price.
- Find the monthly payment.
✅ Solution:
- Amount Financed:
\[\begin{align} \text{Amount Financed} &=\text{Cash Price}-\text{Down Payment} \nonumber \\[4pt] \text{Amount Financed} &=($\text{1,048.98)}-($\text{200)} \nonumber \\[4pt] \end{align}\]
\[\boxed {\text{Amount Financed}=$\text{848.98}}\nonumber \]
- Finance Charge:
\[I=P\cdot r\cdot t\nonumber \]
We know that \(P=$\text{848.98};~r=0.2199;~t=0.5\), \((\text{6 months = 0.5 year})\), so
\[\begin{align} I &= ($\text{848.98})\cdot(0.2199)\cdot(1)\nonumber\\[4pt] I &= $\text{93.345351} \nonumber \\[4pt] \end{align}\]
\[\boxed {\text{Finance Charge}=$\text{93.35}}\nonumber \]
- Total Installment Price:
\[\begin{align} \text{Total Installment Price} &=\text{Amount Financed} + \text{Finance Charge} \nonumber \\[4pt] \text{Total Installment Price} &=($\text{848.98)} + ($\text{93.35)} \nonumber \\[4pt] \end{align}\]
\[\boxed {\text{Total Installment Price}=$\text{942.33}}\nonumber \]
- Monthly Payment:
\[\begin{align}\text{Monthly Payment} &= \frac{\text{Total Installment Price}}{\text{Number of Months}} \nonumber \\[8pt] \text{Monthly Payment} &= \frac{($\text{942.33)}}{(6)} \nonumber \\[8pt] \text{Monthly Payment} &= \text{157.055} \nonumber \\[8pt]\end{align}\]
\[\boxed {\text{Monthly Payment}=$\text{157.06}}\nonumber \]
Refer to Example 4.6.1. Jamal noticed that the retailer is running a promotion of 0% financing, same as cash, for 6 months on all purchases of $500 or more. Assuming these new conditions and the same down payment of $200, answer the same questions below:
- Find the amount financed.
- Find the finance charge.
- Find the total installment price.
- Find the monthly payment.
✅ Solution:
- Amount Financed:
\[\begin{align} \text{Amount Financed} &=\text{Cash Price}-\text{Down Payment} \nonumber \\[4pt] \text{Amount Financed} &=($\text{1,048.98)}-($\text{200)} \nonumber \\[4pt] \end{align}\]
\[\boxed {\text{Amount Financed}=$\text{848.98}}\nonumber \]
- Finance Charge:
\[I=P\cdot r\cdot t\nonumber \]
We know that \(P=$\text{848.98};~r=0;~t=0.5\), \((\text{6 months = 0.5 year})\), so
\[\begin{align} I &= ($\text{848.98})\cdot(0)\cdot(0.5)\nonumber\\[4pt] \end{align}\]
\[\boxed {\text{Finance Charge}=$\text{0}}\nonumber \]
- Total Installment Price:
\[\begin{align} \text{Total Installment Price} &=\text{Amount Financed} + \text{Finance Charge} \nonumber \\[4pt] \text{Total Installment Price} &=($\text{848.98)} + ($\text{0)} \nonumber \\[4pt] \end{align}\]
\[\boxed {\text{Total Installment Price}=$\text{848.98}}\nonumber \]
- Monthly Payment:
\[\begin{align}\text{Monthly Payment} &= \frac{\text{Total Installment Price}}{\text{Number of Months}} \nonumber \\[8pt] \text{Monthly Payment} &= \frac{($\text{848.98)}}{(6)} \nonumber \\[8pt] \text{Monthly Payment} &= \text{141.49666666667} \nonumber \\[8pt]\end{align}\]
\[\boxed {\text{Monthly Payment}=$\text{141.50}}\nonumber \]
So, let's examine the two previous examples more closely:
- In Example #4.6.1, APR = 21.99%, Finance Charge/Interest: $93.35; Monthly payment: $157.06 for 6 months; Total installment price: $942.33
- In Example #4.6.2, APR = 0%, Finance Charge/Interest: $0; Monthly payment: $141.50* for 6 months; Total installment price: $849.00*
These two examples illustrate an important lesson in consumer finance: Short-term, 0% interest promotions can be a smart option only if you can comfortably afford the higher payments. If you could not afford a $141.50 payment and you wanted a longer loan term, let's say 12 months, then your finance charge is $186.69 with a monthly payment of $86.31. So, which option would you rather have? The finance charge is what really tells you the true cost of borrowing, not the monthly payment. The difference in all of these different scenarios, shows how the structure of the loan, not the price of the item, determines the final cost.
* Note: In Example #4.6.2, the monthly payment is $141.50 for the first five months and $141.48 for the final month. This happens because, in a fixed installment loan, the total installment price divided by the number of payments does not always produce an amount that rounds exactly to the nearest cent/penny. As a result, the last payment is sometimes adjusted slightly so the total of all payments matches the exact amount owed.
0% Deferred Interest (Most Store Cards)
Many retail stores advertise “same as cash” 0% financing on purchases over a certain amount, but most of these deals use a system called deferred interest. Example #4.6.2 is based on this model, which can be risky if the borrower is not careful. Here’s how deferred interest works:
- You truly pay 0% interest only if you pay off the entire balance before the promotional period ends.
- If you fail to do so, even by just $1, the lender adds all the interest that would have been charged from day one.
- If you miss or skip a payment, the promotional terms are canceled immediately, and the lender charges all accumulated interest plus a late fee, usually between $25–$40.
In other words, the “deferred interest” is the interest that would have been applied from the beginning at the lender’s standard APR, often between 25%–30% or higher. Missing a payment or failing to pay the full balance by the deadline means this entire amount is suddenly added to your loan. This can leave you owing months of back interest all at once. Late or missed payments can also damage your credit score. A reported late payment often lowers a credit score by 50–150 points, which may cause higher interest rates on future loans or even lead to being denied new credit.
Priya buys an engagement ring from Kay Jewelers for $3,200.00. He puts $500 down and finances the remainder through Kay’s financing program at 24.99% APR for 36 months.
- Find the amount financed.
- Find the finance charge.
- Find the total installment price.
- Find the monthly payment.
✅ Solution:
- Amount Financed:
\[\begin{align} \text{Amount Financed} &=\text{Cash Price}-\text{Down Payment} \nonumber \\[4pt] \text{Amount Financed} &=($\text{3,200.00)}-($\text{500)} \nonumber \\[4pt] \end{align}\]
\[\boxed {\text{Amount Financed}=$\text{2,700.00}}\nonumber \]
- Finance Charge:
\[I=P\cdot r\cdot t\nonumber \]
We know that \(P=$\text{2,700.00};~r=0.2499;~t=3\), \((\text{36 months = 3 year})\), so
\[\begin{align} I &= ($\text{2,700.00})\cdot(0.2499)\cdot(3)\nonumber\\[4pt] \end{align}\]
\[\boxed {\text{Finance Charge}=$\text{2,024.19}}\nonumber \]
- Total Installment Price:
\[\begin{align} \text{Total Installment Price} &=\text{Amount Financed} + \text{Finance Charge} \nonumber \\[4pt] \text{Total Installment Price} &=($\text{2,700.00)} + ($\text{2,024.19)} \nonumber \\[4pt] \end{align}\]
\[\boxed {\text{Total Installment Price}=$\text{4,724.19}}\nonumber \]
- Monthly Payment:
\[\begin{align}\text{Monthly Payment} &= \frac{\text{Total Installment Price}}{\text{Number of Months}} \nonumber \\[8pt] \text{Monthly Payment} &= \frac{($\text{4,724.19)}}{(36)} \nonumber \\[8pt] \text{Monthly Payment} &= \text{131.2275} \nonumber \\[8pt]\end{align}\]
\[\boxed {\text{Monthly Payment}=$\text{131.23}}\nonumber \]
Yvette buys a 3‑seat leather power‑reclining home theater set for $4,999.00. She uses the store’s financing program at 25.74% APR, with no down payment, over 72 months.
- Find the amount financed.
- Find the finance charge.
- Find the total installment price.
- Find the monthly payment.
✅ Solution:
- Amount Financed:
\[\begin{align} \text{Amount Financed} &=\text{Cash Price}-\text{Down Payment} \nonumber \\[4pt] \text{Amount Financed} &=($\text{4,999.00)}-($\text{0)} \nonumber \\[4pt] \end{align}\]
\[\boxed {\text{Amount Financed}=$\text{4,999.00}}\nonumber \]
- Finance Charge:
\[I=P\cdot r\cdot t\nonumber \]
We know that \(P=$\text{4,999.00};~r=0.2574;~t=6\), \((\text{12 months = 1 year})\), so
\[\begin{align} I &= ($\text{4,999.00})\cdot(0.2574)\cdot(6)\nonumber\\[4pt] I &= $\text{7,720.4556} \nonumber \\[4pt] \end{align}\]
\[\boxed {\text{Finance Charge}=$\text{7,720.46}}\nonumber \]
- Total Installment Price:
\[\begin{align} \text{Total Installment Price} &=\text{Amount Financed} + \text{Finance Charge} \nonumber \\[4pt] \text{Total Installment Price} &=($\text{4,999.00)} + ($\text{7,720.46)} \nonumber \\[4pt] \end{align}\]
\[\boxed {\text{Total Installment Price}=$\text{12,719.46}}\nonumber \]
- Monthly Payment:
\[\begin{align}\text{Monthly Payment} &= \frac{\text{Total Installment Price}}{\text{Number of Months}} \nonumber \\[8pt] \text{Monthly Payment} &= \frac{($\text{12,719.46)}}{(72)} \nonumber \\[8pt] \text{Monthly Payment} &= \text{176.65916666667} \nonumber \\[8pt]\end{align}\]
\[\boxed {\text{Monthly Payment}=$\text{176.66}}\nonumber \]
The last two examples illustrate one of the many important lessons in consumer finance: A longer loan with interest can cost much more overall than a shorter loan. It also shows why stretching payments over more months reduces the monthly payment, but increases the total cost
For Exercises 1 & 2:
- Find the amount financed.
- Find the finance charge.
- Find the total installment price.
- Find the monthly payment.
- Val purchases a MacBook Air M2 at the Apple Store for $1,099.00. She uses the Apple Card Monthly Installments program at 21.24% APR (typical for lower‑credit tiers). She puts $100 down and finances for 12 months.
- Roger buys a premium 6‑piece solid‑wood bedroom set from a local furniture store for $6,899.99. He puts $900 down, and the store finances the balance at 24.99% APR for 60 months.
- Answers
-
- a) Amount Financed = $999.99; b) Finance Charge = $212.19; c) Total Installment Price = $1211.19; d) Monthly Payment = $100.93.
- a) Amount Financed = $5999.99; b) Finance Charge = $7,496.85; c) Total Installment Price = $13,496.84; d) Monthly Payment = $224.95.