AP Business with Personal Finance · Lesson 3

Loans, the true cost of borrowing and paying off debt

Know Know it

Most installment loans are amortized: each fixed monthly payment covers that month’s interest first and the rest pays down the principal. Early payments are mostly interest; later ones are mostly principal. The total cost of a loan is the monthly payment times the number of payments, and the total interest is that total minus the amount borrowed. A longer term lowers the monthly payment but raises the total interest, because the balance stays high for longer. A larger down payment means borrowing less, so it lowers both.

Lenders judge a borrower by the five Cs: character (the record of repaying, seen in the credit report and score), capacity (income compared with debts), capital (savings and assets), collateral (property that secures the loan) and conditions (the purpose of the loan and the economy). Capacity is often measured with the debt-to-income ratio: monthly debt payments divided by gross monthly income. A borrower with little history may need a cosigner, who must repay if the borrower does not.

Some borrowing is very expensive. Payday loans charge a fee that looks small, such as 15 dollars per 100 borrowed for two weeks, but works out to an APR of several hundred percent. Rent-to-own deals and some buy now, pay later plans can add high fees or late charges. Federal student loans usually charge lower, fixed rates than private ones; on a subsidized federal loan the government pays the interest while the student is in school, while on an unsubsidized loan interest builds from the start.

To pay down several debts, list them and pay at least the minimum on each. The debt avalanche puts every extra dollar on the debt with the highest interest rate, which saves the most money. The debt snowball clears the smallest balance first, for quick wins that keep people motivated. Consolidation, one new loan that pays off several old ones, can help if its rate is lower. If debts become unmanageable, a nonprofit credit counselor can help; bankruptcy is a legal last resort that stays on a credit report for up to ten years.

Trap A lower monthly payment is not a cheaper loan

Stretching a loan over more months makes each payment smaller, but you pay interest for longer, so the total cost goes up. To compare loans, multiply each payment by the number of payments and compare the totals, not just the monthly amounts.

Worked example Easy

Ivy borrows 8,000 dollars for a fictional used car. She will make 36 monthly payments of 245.19 dollars. How much interest will she pay over the life of the loan?

  1. 8,826.84 dollars
  2. 826.84 dollarsAnswer
  3. 1,560.00 dollars
  4. 245.19 dollars

How to solve it

  1. Total paid = payment x number of payments = 245.19 x 36 = 8,826.84 dollars.
  2. Interest = total paid - amount borrowed.
  3. 8,826.84 - 8,000 = 826.84 dollars.

Why each choice is right or wrong

  • A. Incorrect. 8,826.84 dollars is the total of all payments, 245.19 x 36, which includes the 8,000 dollars borrowed.
  • B. Correct. Total paid = 245.19 x 36 = 8,826.84 dollars, and interest = 8,826.84 - 8,000 = 826.84 dollars.
  • C. Incorrect. 1,560.00 dollars would be simple interest on the full 8,000 for 3 years at 6.5 percent; her balance falls as she pays, so she pays less.
  • D. Incorrect. 245.19 dollars is one monthly payment, not the interest over all 36 months.

Explain Explain it

Task verbs: compare, evaluate

To compare two loans, work out the total cost of each, then name the trade-off: which one is easier to afford each month and which one costs less in all.

To evaluate whether a borrower can take on a new payment, compute the debt-to-income ratio with and without it, then compare the result with the lender’s limit.

Worked example Medium

Two fictional offers for a 12,000 dollar car loan at the same 6.5 percent APR

OfferTermMonthly payment (dollars)
Offer 148 months284.58
Offer 260 months234.79

How much more does Offer 2 cost in total than Offer 1?

  1. 49.79 dollars
  2. 2,087.40 dollars
  3. 427.56 dollarsAnswer
  4. 1,659.84 dollars

How to solve it

  1. Offer 1 total: 284.58 x 48 = 13,659.84 dollars.
  2. Offer 2 total: 234.79 x 60 = 14,087.40 dollars.
  3. Difference: 14,087.40 - 13,659.84 = 427.56 dollars more for the longer loan.

Why each choice is right or wrong

  • A. Incorrect. 49.79 dollars is the difference in the monthly payments, 284.58 - 234.79, not in the total cost.
  • B. Incorrect. 2,087.40 dollars is Offer 2’s total interest, 14,087.40 - 12,000, not the difference between the offers.
  • C. Correct. Offer 1 totals 284.58 x 48 = 13,659.84 dollars; Offer 2 totals 234.79 x 60 = 14,087.40 dollars; the difference is 427.56 dollars.
  • D. Incorrect. 1,659.84 dollars is Offer 1’s total interest, 13,659.84 - 12,000, not how much more Offer 2 costs.

Evaluate Your turn

Priya earns 4,200 dollars a month before taxes. She already pays 550 dollars a month on a student loan. A fictional lender approves car loans only if a borrower’s total monthly debt payments stay at or below 20 percent of gross monthly income. Calculate her debt-to-income ratio now, and decide whether she can take on a car payment of 290 dollars a month and stay within the lender’s limit. Show your numbers.

Write it, then compare. Nothing you type here is saved or graded.

Compare with a model answer

A full answer does this

  • Calculates her current ratio as about 13 percent
  • Calculates the ratio with the car payment as 20 percent
  • Concludes that she stays within the limit, because 20 percent is not above 20 percent

Model answer

Now: 550 / 4,200 ≈ 0.131, or about 13.1 percent. With the car payment, her monthly debts would be 550 + 290 = 840 dollars, and 840 / 4,200 = 0.20, or 20 percent. The lender allows up to 20 percent, so she can take on the 290 dollar payment, though it would leave her exactly at the limit with no room for more debt.

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