Question

matias needs to know how much he will owe the bank after one year. explain why his math is wrong.
$10,000 × .12 + $99 = $1,299
matias dreams of opening a food truck business. he needs to borrow $10,000 to buy the truck. the $10,000 is called the principal. banks charge interest on the principal. matias’ bank charges? of 12%. that’s a? of 1% per month. after one year, matias will owe interest of 12% of the $10,000 principal. written as a fraction, the? is 12 and the? is 100. so, $10,000 × 12/100 = $1,200. the bank also charges a? application?. matias thinks he will owe $1,200 + $99 = $1,299. what is he missing? matias forgot about the $10,000. he will have to pay the? back, too! he will owe the bank a total of $10,000 + $1,299 = $11,299. the interest and the fee will be $1,299/$11,299 ≈ 11.5% of the total amount owed. that’s a? ratio. the interest and fee are $1,299/$10,000 ≈ 13% of the principal. that’s a? ratio.
simple interest
numerator
unit price
unit rate
principal
part - to - part
fee
denominator

Explanation:

Step1: Identify the total amount owed

The amount owed to the bank includes the principal (the amount borrowed) plus the interest and any fees. The principal is $10,000. The interest is calculated as LXI0 and there's a $99 fee. So the interest and fee total \( \$1,200 + \$99=\$1,299 \), but this is just the additional amount on top of the principal.

Step2: Explain Matias' mistake

Matias only calculated the interest and the fee (\( \$10,000 \times 0.12+\$99=\$1,299 \)) but forgot to add the original principal (\$10,000) to this amount. The total amount owed should be the principal plus the interest and the fee. So the correct total is LXI1, not just \$1,299.

Answer:

Matias forgot to include the principal (\$10,000) in the total amount owed. The total amount owed to the bank is the principal plus the interest and the fee, so it should be \$10,000 + (\$10,000×0.12 + \$99)=\$11,299, not \$1,299.