3. The formula below finds the monthly payment for a loan (car, mortgage, student): a. Assume you decide to take a 7-year car loan, with 3.875% APR paid monthly. Remember that 3.875% is not advertised in a monthly format. Insert the numbers you have so far into the formula above and simplify as much as possible. (Note: simplify means to calculate the parts of the equation that you can so far.) If necessary, round to the thousandths place. b. Use your simplified formula from above to answer: What is the largest amount you can borrow for the car if you can afford a $440/month payment?
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
3. The formula below finds the monthly payment for a loan (car, mortgage, student):
a. Assume you decide to take a 7-year car loan, with 3.875% APR paid monthly. Remember that 3.875% is not advertised in a monthly format. Insert the numbers you have so far into the formula above and simplify as much as possible. (Note: simplify means to calculate the parts of the equation that you can so far.) If necessary, round to the thousandths place.
b. Use your simplified formula from above to answer: What is the largest amount you can borrow for the car if you can afford a $440/month payment?
![### Loan Payment Formula
To find the monthly payment for a loan (such as a car loan, mortgage, or student loan), you can use the following formula:
\[
P = I \left( \frac{r}{1 - (1 + r)^{-n}} \right)
\]
Where:
- \( P \) = **Monthly payment**
- \( I \) = **Initial loan amount borrowed**
- \( r \) = **Monthly interest rate written in decimal form**
- \( n \) = **Number of months to pay off the loan**
#### Explanation of Variables:
- **Monthly Payment (P)**: The fixed amount paid every month to repay the loan.
- **Initial Loan Amount (I)**: The total amount borrowed at the beginning.
- **Monthly Interest Rate (r)**: The interest rate per month, expressed as a decimal (e.g., for an annual interest rate of 6%, the monthly rate \( r \) would be \( 0.06 / 12 = 0.005 \)).
- **Number of Months (n)**: The total number of monthly payments to fully repay the loan.
This formula helps calculate how much needs to be paid each month based on the initial loan amount, the interest rate, and the loan term (in months).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0ac09dd4-4ef1-4547-8e59-df536754c306%2F6bd801cb-bf38-4bc9-a47e-f920a767ac25%2Fl7zuqy_processed.jpeg&w=3840&q=75)
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