Use the given yearly payment schedule. a. What is the loan...

Use the given yearly payment schedule. a. What is the loan amount? b. What is the length of the loan? c. What is the monthly payment? d. What is the total interest paid? e. Construct a scatterplot using the data points (year, loan balance). f. Write a linear regression equation that approximates the year/loan balance relationship. Round to nearest hundredth. g. Write a quadratic regression equation that approximates the year/loan balance relationship. Round to nearest hundredth. h. Write a cubic regression equation that approximates the year/loan balance relationship. Round to the nearest hundredth. $$\begin{array}{|c|c|c|c|}\hline \text { Year } & {\text { Principal Paid }} & {\text { Interest Paid }} & {\text { Loan Balance }} \\ \hline 0 & {} & {} &{\$ 10,000.00} \\ \hline 1 & {\$ 680.52} & {$ 775.41} &{\$ 9,319.48} \\ \hline 2 & {$ 737.01} & {$ 718.92} &{\$ 8,582.47} \\ \hline 3 & {$ 798.18} & {$ 657.75} &{\$ 7,784.29} \\ \hline 4 & {$ 864.43} & {$ 591.50} &{\$ 6,919.86} \\ \hline 5 & {$ 936.17} & {$ 519.76} &{\$ 5,983.69} \\ \hline 6 & {$ 1,013.88} & {\$ 442.05} &{\$ 4,969.81} \\ \hline 7 & {$ 1,098.03} & {\$ 357.90} &{\$ 3,871.78} \\ \hline 8 & {$ 1,189.16} & {\$ 266.77} &{\$ 2,682.62} \\ \hline 9 & {$ 1,287.86} & {\$ 168.07} &{\$ 1,394.76} \\ \hline 10 & {$ 1,394.76} & {\$ 61.18} &{\$ 0.00} \\ \hline\end{array}$$

Use the given yearly payment schedule.
a. What is the loan amount?
b. What is the length of the loan?
c. What is the monthly payment?
d. What is the total interest paid?
e. Construct a scatterplot using the data points (year, loan balance).
f. Write a linear regression equation that approximates the year/loan balance relationship. Round to nearest hundredth.
g. Write a quadratic regression equation that approximates the year/loan balance relationship. Round to nearest hundredth.
h. Write a cubic regression equation that approximates the year/loan balance relationship. Round to the nearest hundredth.

$$\begin{array}{|c|c|c|c|}\hline \text { Year } & {\text { Principal Paid }} & {\text { Interest Paid }} & {\text { Loan Balance }} \\ \hline 0 & {} & {} &{\$ 10,000.00} \\ \hline 1 & {\$ 680.52} & {$ 775.41} &{\$ 9,319.48} \\ \hline 2 & {$ 737.01} & {$ 718.92} &{\$ 8,582.47} \\ \hline 3 & {$ 798.18} & {$ 657.75} &{\$ 7,784.29} \\ \hline 4 & {$ 864.43} & {$ 591.50} &{\$ 6,919.86} \\ \hline 5 & {$ 936.17} & {$ 519.76} &{\$ 5,983.69} \\ \hline 6 & {$ 1,013.88} & {\$ 442.05} &{\$ 4,969.81} \\ \hline 7 & {$ 1,098.03} & {\$ 357.90} &{\$ 3,871.78} \\ \hline 8 & {$ 1,189.16} & {\$ 266.77} &{\$ 2,682.62} \\ \hline 9 & {$ 1,287.86} & {\$ 168.07} &{\$ 1,394.76} \\ \hline 10 & {$ 1,394.76} & {\$ 61.18} &{\$ 0.00} \\ \hline\end{array}$$

Key Concepts

Cubic Regression

Cubic regression involves fitting a third-degree polynomial to data. This method provides even greater flexibility to model complex, non-linear relationships, which can be useful when approximating data that changes in multiple phases or with inflection points.

Quadratic Regression

Quadratic regression fits a parabolic curve to data. It is employed when the relationship between variables has curvature that is not captured by a straight line, offering a better fit in some non-linear scenarios.

Linear Regression

Linear regression is a statistical method for modeling the relationship between a dependent variable and one independent variable using a straight line. It is useful for approximating trends in data, such as the decrease in loan balance over time.

Data Visualization (Scatter Plot)

A scatter plot is a graphical representation that uses plotted points to display the relationship between two variables. In the context of loan repayment, it can show how the remaining balance changes over time.

Loan Amortization

This concept involves breaking down a loan into a schedule of fixed payments over time, where each payment is divided into principal and interest portions. It tracks the gradual reduction of the outstanding balance until the loan is fully paid off.

Payment Calculation

This involves determining the periodic payment amount required to repay a loan, often derived from the loan amount, interest rate, and the number of payment periods. It includes conversions between annual and monthly payments when necessary.

Loan Term Determination

This pertains to identifying the duration over which a loan is repaid, based on the payment schedule. It indicates how many periods (years, months, etc.) constitute the full repayment duration.

Total Interest Calculation

This is the process of adding up all the interest paid during the life of the loan to determine the overall cost of borrowing, which goes beyond just repaying the principal.

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