Personal Financial Literacy>Solving Problems with Interest Rates and Loan Lengths Affecting Credit Costs(TEKS.Math.8.12.A)
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Texas 8th Grade Math › Personal Financial Literacy>Solving Problems with Interest Rates and Loan Lengths Affecting Credit Costs(TEKS.Math.8.12.A)
Loan Option A: $10,000 at 6% annual interest for 3 years. Loan Option B: $10,000 at 4% annual interest for 5 years. Which loan costs more in total interest?
Loan Option A costs more in total interest because its rate is higher.
Both options cost the same total interest.
Loan Option B costs more in total interest because the lower rate is applied for more years.
Not enough information without knowing monthly payments.
Explanation
Use simple interest $I = P r t$. For A: $I_A = 10000 \times 0.06 \times 3 = 1800$. For B: $I_B = 10000 \times 0.04 \times 5 = 2000$. Since $2000 > 1800$, B costs more. A higher rate increases cost, and more years increase cost; here the longer time outweighs the lower rate.
Car loan comparison: Option A is $15,000 at 7.5% annual interest for 4 years. Option B is $15,000 at 5.5% annual interest for 6 years. Which loan costs more in total interest?
Option A costs more in total interest.
They cost the same total interest.
Option B has a lower monthly payment, so it must cost less overall.
Option B costs more in total interest because it accrues interest for more years even at a lower rate.
Explanation
Simple interest: $I_A = 15000 \times 0.075 \times 4 = 4500$. $I_B = 15000 \times 0.055 \times 6 = 4950$. Since $4950 > 4500$, Option B costs more in total interest. Longer terms generally increase total interest even if the rate is lower.
Two loans have the same principal and interest rate. Loan A is for 3 years; Loan B is for 6 years. How does loan length affect monthly payments and total interest?
A longer term raises the monthly payment but reduces total interest.
A longer term usually lowers the monthly payment but increases the total interest paid over the life of the loan.
Loan length does not change monthly payments if the rate stays the same.
A longer term lowers both the monthly payment and the total interest because payments are spread out.
Explanation
With the same principal and rate, spreading payments over more years generally lowers each monthly payment but increases total interest, since interest accrues for a longer time. In simple interest terms, $I = P r t$ grows with larger $t$.
Personal loan: Option A is $8,000 at 9% annual interest for 2 years. Option B is $8,000 at 6% annual interest for 4 years. Which option costs more in total interest?
Option B costs more in total interest.
Option A costs more because 9% is a higher rate.
They cost the same total interest.
You cannot tell without knowing the monthly payment amount.
Explanation
Compute simple interest. $I_A = 8000 \times 0.09 \times 2 = 1440$. $I_B = 8000 \times 0.06 \times 4 = 1920$. Since $1920 > 1440$, Option B costs more overall. A lower rate can still cost more if the term is longer.
Laptop financing: Option A is $2,400 at 12% annual interest for 1 year. Option B is $2,400 at 8% annual interest for 3 years. Which loan costs more in total interest?
Option A costs more because 12% is higher than 8%.
Option B costs more because it runs for more years even at a lower rate.
They cost the same total interest.
Option B has smaller monthly payments, so it costs less overall.
Explanation
Simple interest: $I_A = 2400 \times 0.12 \times 1 = 288$. $I_B = 2400 \times 0.08 \times 3 = 576$. Since $576 > 288$, Option B costs more. Longer terms generally increase total interest even when the rate is lower.