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Evaluate financial decisions using mathematical reasoning

Financial decision-making involves translating prices, discounts, taxes, fees, payment schedules, interest rates, and inflation into comparable quantities such as total cost, net gain, cost per unit, and effective rate. Using percentages, proportional reasoning, simple and compound interest, and tables, graphs, or formulas, a learner compares purchasing, saving, borrowing, and basic investment alternatives while accounting for time and recognizing that a lower periodic payment can result in a higher total cost; continuous compounding, advanced risk models, and complex financial instruments are not included.

Detailed Explanation: Evaluate financial decisions using mathematical reasoning

To evaluate a financial decision, translate each option into a comparable quantity—usually the total cost. Apply discounts and taxes in the correct order, then compare the results.

Example

A laptop has a listed price of 900$.

  • Option A: Pay immediately and receive a 15%15\% discount. Then pay 8%8\% sales tax.
  • Option B: Make 1212 monthly payments of 82andpayaand pay a$40$ setup fee.

Which option costs less?

Step 1: Find the discount amount

The discount is

15% of $900=0.15($900)=$135.15\% \text{ of } \$900=0.15(\$900)=\$135.

Subtract the discount from the listed price:

$900$135=$765.\$900-\$135=\$765.

So, the price before tax is 765$.

Step 2: Find the sales tax

The tax is based on the discounted price:

8% of $765=0.08($765)=$61.20.8\% \text{ of } \$765=0.08(\$765)=\$61.20.

Add the tax:

$765+$61.20=$826.20.\$765+\$61.20=\$826.20.

Therefore, the total cost of Option A is

$826.20.\boxed{\$826.20}.

Step 3: Find the total cost of the payment plan

There are 1212 payments of 82$:

12($82)=$984.12(\$82)=\$984.

Add the setup fee:

$984+$40=$1, ⁣024.\$984+\$40=\$1,\!024.

Therefore, the total cost of Option B is

$1, ⁣024.\boxed{\$1,\!024}.

Step 4: Compare the totals

Subtract the lower total from the higher total:

$1, ⁣024$826.20=$197.80.\$1,\!024-\$826.20=\$197.80.

The payment plan costs 197.80}$ more overall.

Even though 82$ per month may seem manageable, the total cost is higher. If the buyer can afford to pay immediately, Option A is the better financial decision because it costs less in total.

Learn by doing: Evaluate financial decisions using mathematical reasoning

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Financial Literacy - Interest and Fees - Simple - Interest Plus Fee to Equivalent Interest Rate


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