Questions: A. Answer True or False for each statement. Use your notes to help you draft mathematically sound explanations for each of the following. It may be helpful to provide examples in each case. Answers must be in your own words 1. In the formula i=Pr t, i and r are the same things. 2. A 720-day loan means that it needs to be paid back in two years. 3. A 700 down payment means that P=700 in the formula A=P+i. 4. A student took out a 9-month 600 loan from a lender. If the interest is 10.5%, the student will owe more than 650.

A. Answer True or False for each statement. Use your notes to help you draft mathematically sound explanations for each of the following. It may be helpful to provide examples in each case. Answers must be in your own words
1. In the formula i=Pr t, i and r are the same things.
2. A 720-day loan means that it needs to be paid back in two years.
3. A 700 down payment means that P=700 in the formula A=P+i.
4. A student took out a 9-month 600 loan from a lender. If the interest is 10.5%, the student will owe more than 650.

Transcript text: A. Answer True or False for each statement. Use your notes to help you draft mathematically sound explanations for each of the following. It may be helpful to provide examples in each case. Answers must be in your own words 1. In the formula $i=P r t, i$ and $r$ are the same things. 2. A 720 -day loan means that it needs to be paid back in two years. 3. A $\$ 700$ down payment means that $P=700$ in the formula $A=P+i$. 4. A student took out a 9-month $\$ 600$ loan from a lender. If the interest is $10.5 \%$, the student will owe more than $\$ 650$.

Solution

Solution Steps

Solution Approach

The formula $ i = P \cdot r \cdot t $ represents simple interest, where $ i $ is the interest, $ P $ is the principal amount, $ r $ is the rate of interest, and $ t $ is the time period. $ i $ and $ r $ are not the same; $ i $ is the result of the calculation, while $ r $ is a component of the formula.
A 720-day loan is equivalent to 720/365 years. We need to check if this is equal to 2 years.
In the formula $ A = P + i $, $ P $ represents the principal amount, not the down payment. A down payment is an initial payment made when something is bought on credit, and it does not necessarily equal the principal in the formula.
To determine if the student will owe more than $650, calculate the interest on a $600 loan at 10.5% for 9 months and add it to the principal to see if the total exceeds $650.

Step 1: Evaluate Statement 1

In the formula $ i = P \cdot r \cdot t $, $ i $ (interest) and $ r $ (rate) are not the same. The output confirms that $ \text{statement\_1} = \text{False} $.

Step 2: Evaluate Statement 2

A 720-day loan is calculated as follows: \[ \text{years} = \frac{720}{365} \approx 1.9726 \] Since $ 1.9726 $ is not equal to $ 2 $, the output confirms that $ \text{statement\_2} = \text{False} $.

Step 3: Evaluate Statement 3

In the formula $ A = P + i $, $ P $ represents the principal amount, not the down payment. Therefore, $ \text{statement\_3} = \text{False} $.

Step 4: Evaluate Statement 4

To determine if the student will owe more than $650, we calculate the interest on a $600 loan at a rate of $ 10.5\% $ for $ 9 $ months: \[ \text{interest} = 600 \cdot 0.105 \cdot \frac{9}{12} = 47.25 \] Adding this interest to the principal gives: \[ \text{total amount} = 600 + 47.25 = 647.25 \] Since $ 647.25 < 650 $, the output confirms that $ \text{statement\_4} = \text{False} $.