Calculating Total Loan Repayment Costs Under Different Rates and Periods(TEKS.Math.8.12.B)
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Texas 8th Grade Math › Calculating Total Loan Repayment Costs Under Different Rates and Periods(TEKS.Math.8.12.B)
Credit card balance: \$2,520 at 18% APR. Minimum payment: \$75 per month. Online calculator excerpt after 12 months:
- Total paid: \$900
- Interest paid: \$540
- Principal paid: \$360
- Remaining balance: \$2,160
How much interest did Maya pay during the first 12 months?
\$360
\$540
\$900
\$2,160
Explanation
From the amortization output, interest paid is given directly as \$540. It also matches total paid minus principal paid (900 − 360 = 540). With high APR and minimum payments, most of the payment goes to interest, so the balance stays high.
Borrowing \$1,000 for a phone. Two payoff options from an online calculator: Option A: 12-month installment at 18% APR
- Monthly payment: \$92
- Total paid: \$1,104
- Total interest: \$104 Option B: 24-month installment at 12% APR
- Monthly payment: \$47
- Total paid: \$1,128
- Total interest: \$128
Which option has the lower total cost to repay the loan?
Option A: \$1,104
Option B: \$1,128
Both cost \$1,000
Option B has lower cost because $47 < $92
Explanation
Total cost is the total of all payments. Option A costs \$1,104, which is less than Option B's \$1,128. A lower monthly payment does not mean a lower total cost; the longer term adds more interest.
Easy-access cash advance: \$500 at very high APR. Online calculator shows a \$75 fee each 2-week rollover if not repaid. After 6 weeks (3 rollovers):
- Total fees paid: \$225
- Principal still owed: \$500
If the loan is rolled over for 6 weeks and nothing is paid toward principal, how much has been paid in interest/fees?
\$75
\$500
\$725
\$225
Explanation
Each rollover adds a \$75 fee. Three rollovers cost 3 × \$75 = \$225 in fees, while the \$500 principal remains. High fees and no principal reduction make these loans very expensive.
Installment loan for a bike: \$1,200 at 15% APR, 24 months. Online calculator:
- Monthly payment: \$58
- Total paid: \$1,392
- Total interest: \$192
What is the total cost of repaying this loan?
\$1,200
\$1,258
\$1,392
\$192
Explanation
Total cost is the sum of all payments over the term, which the calculator gives as \$1,392. This equals principal (\$1,200) plus interest (\$192). APR and term determine both the payment and total interest.
Credit card balance: \$2,400 at 22% APR. Minimum payment: \$50 per month. Online calculator excerpt after 6 months:
- Total paid: \$300
- Interest paid: \$260
- Principal paid: \$40
- Remaining balance: \$2,360
Which statement is best supported by this amortization excerpt?
The balance drops by \$50 each month.
Most of each minimum payment goes to interest in the first months.
Paying the minimum will pay off the card in 6 months.
The APR doesn't affect how long it takes to repay.
Explanation
In 6 months, \$300 was paid but only \$40 reduced the balance; \$260 was interest. That shows most of each minimum payment is interest at first. High APR and small minimums keep balances high and extend repayment time.