Question

1. jordan is taking out a 2 - week payday loan for $600. he will be charged $95 interest for the 2 - week loan. what is the apr for this loan?
2. juliana is taking out an $8,700, 3 - year loan with an apr of 2.31%. what will be the monthly payment for this loan? round to the nearest cent.

Explanation:

Problem 9:

Step1: Recall APR formula

APR (Annual Percentage Rate) for a short - term loan can be calculated using the formula \(APR=\frac{Interest\times365}{Principal\times Time}\), where time is in days. For a 2 - week loan, the time \(t = 14\) days. The principal \(P=\$600\) and the interest \(I = \$95\).

Step2: Substitute values into the formula

First, calculate the numerator: \(Interest\times365=95\times365 = 34675\)
Then, calculate the denominator: \(Principal\times Time=600\times14 = 8400\)
Now, find the APR: \(APR=\frac{34675}{8400}\approx4.128\) or \(412.8\%\) (we multiply by 100 to get the percentage)

Step1: Recall the monthly payment formula for a loan

The formula for the monthly payment \(M\) of a loan is \(M=\frac{P\times\frac{r}{12}(1 + \frac{r}{12})^{n}}{(1+\frac{r}{12})^{n}-1}\), where \(P\) is the principal amount of the loan, \(r\) is the annual percentage rate (APR) (in decimal form), and \(n\) is the total number of payments (number of years \(\times12\)).
Given that \(P = \$8700\), the APR \(r=2.31\%=0.0231\), and the number of years \(y = 3\), so the number of payments \(n=3\times12 = 36\).

Step2: Calculate \(\frac{r}{12}\)

\(\frac{r}{12}=\frac{0.0231}{12}=0.001925\)

Step3: Calculate \((1 + \frac{r}{12})^{n}\)

\((1 + 0.001925)^{36}\approx1.072\) (using a calculator to compute the power)

Step4: Calculate the numerator \(P\times\frac{r}{12}(1 + \frac{r}{12})^{n}\)

\(8700\times0.001925\times1.072\)
First, \(8700\times0.001925 = 16.7475\)
Then, \(16.7475\times1.072\approx17.95\)

Step5: Calculate the denominator \((1+\frac{r}{12})^{n}-1\)

\(1.072 - 1=0.072\)

Step6: Calculate the monthly payment \(M\)

\(M=\frac{17.95}{0.072}\approx249.31\) (rounded to the nearest cent)

Answer:

The APR for the loan is approximately \(412.8\%\)

Problem 10: