e. Discuss the relationship between the total interest, loan amount and monthly payment from the graphic below.
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However, generally speaking, the total interest paid on a loan is directly related to the loan amount and the monthly payment. If the loan amount is higher, the total interest paid will also be higher, assuming the interest rate and loan term remain constant. Show more…
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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. $$\begin{array}{|c|c|c|c|}\hline \text { Year } & {\text { Principal Paid }} & {\text { Interest Paid }} & {\text { Loan Balance }} \\ \hline 0 & {} & {} &{\$ 10,000.00} \\ \hline 1 & {\$ 680.52} & {$ 775.41} &{\$ 9,319.48} \\ \hline 2 & {$ 737.01} & {$ 718.92} &{\$ 8,582.47} \\ \hline 3 & {$ 798.18} & {$ 657.75} &{\$ 7,784.29} \\ \hline 4 & {$ 864.43} & {$ 591.50} &{\$ 6,919.86} \\ \hline 5 & {$ 936.17} & {$ 519.76} &{\$ 5,983.69} \\ \hline 6 & {$ 1,013.88} & {\$ 442.05} &{\$ 4,969.81} \\ \hline 7 & {$ 1,098.03} & {\$ 357.90} &{\$ 3,871.78} \\ \hline 8 & {$ 1,189.16} & {\$ 266.77} &{\$ 2,682.62} \\ \hline 9 & {$ 1,287.86} & {\$ 168.07} &{\$ 1,394.76} \\ \hline 10 & {$ 1,394.76} & {\$ 61.18} &{\$ 0.00} \\ \hline\end{array}$$
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Loan Calculations and Regression
Sheryl E.
A bank offers a $\$ 25,000$ loan at an interest rate of 7.7$\%$ that can be paid back over 2 to 10 years. a. Write the monthly payment formula for this loan situation. Let $t$ represent the number of years from 2 to 10 inclusive. b. Write the total interest formula for this loan situation. Let $t$ represent the number of years from 2 to 10 inclusive. c. Construct a graph. Let the indendent variable represent years and the dependent variable represent the interest paid. d. Use your graph to estimate the interest for a 6$\frac{1}{2}$ -year loan.
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