Question

1. lavonda took out a $7,500 loan with an apr of 3.875% and agreed to pay it back monthly over 6 years. how many monthly payments did she make?
2. solomon is taking out a $15,320, 2-year loan with an apr of 3.29%. what will be the finance charge for this loan to the nearest dollar?
3. reggie needs a quick x-dollar loan until his next payday in 2 weeks to take advantage of a sale on ski equipment. the bank would take too long on the paperwork, so he goes to a pawnshop. the pawnshop will only lend him 25% of the value of his collateral. express algebraically the amount of collateral reggie must use for this loan.
4. olivia is considering membership to the regional teachers’ credit union so that she can save money on a loan. the credit union will lend her $8,000 for 3 years at 2.25% apr. the same loan at her savings bank has an apr of 2.9%. how much would olivia save in finance charges if she joined the credit union and took out her loan there? round to the nearest ten dollars.

Explanation:

Question 11:

Step1: Determine the number of months

To find the number of monthly payments, we know that 1 year has 12 months. So for 6 years, we calculate the total number of months by multiplying the number of years by 12.
The formula is: Number of months = Number of years × 12
Given the number of years is 6, so we have \( 6\times12 = 72 \)

Step1: Identify the loan details

The loan amount \( P=\$15320 \), the APR \( r = 3.29\%=0.0329 \), and the loan term \( t = 2 \) years. Since it's a monthly payment, the number of compounding periods per year \( n = 12 \)

Step2: Use the monthly payment formula

The formula for the monthly payment \( M \) of a loan is \( M=\frac{P\times\frac{r}{n}\times(1 + \frac{r}{n})^{nt}}{(1+\frac{r}{n})^{nt}-1} \)
First, calculate \( \frac{r}{n}=\frac{0.0329}{12}\approx0.002742 \)
Then, \( nt=12\times2 = 24 \)
\( (1+\frac{r}{n})^{nt}=(1 + 0.002742)^{24}\approx1.0675 \)
Now, numerator: \( 15320\times0.002742\times1.0675\approx15320\times0.002927\approx44.85 \)
Denominator: \( 1.0675 - 1=0.0675 \)
Then \( M=\frac{44.85}{0.0675}\approx664.44 \) (rounded to the nearest dollar)

Step1: Understand the pawnshop lending

The pawnshop lends 25% of the collateral value. Let the collateral value be \( x \). We know that Reggie needs a \( x \)-dollar loan (wait, actually, Reggie needs a loan, and the pawnshop lends 25% of the collateral. Wait, maybe the problem is: Reggie needs a loan, and the pawnshop will lend him 25% of the collateral value. So if he needs a loan of amount \( L \), then \( 0.25\times\text{collateral}=L \), so collateral \(=\frac{L}{0.25}=4L \)
Assuming the loan amount is \( x \) (as per the problem: "Reggie needs a quick \( x \)-dollar loan"), then the collateral \( C \) is given by \( 0.25C=x \), so \( C = \frac{x}{0.25}=4x \)

Answer:

72

Question 12: