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Loan Repayment Model Demonstration

Loan Repayment Model Demonstration
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2019-02-22 22:24
FunctionTrigonometryProbability & Statistics
This example demonstrates the interest calculation and total repayment amount changes in a loan repayment process. It involves core mathematical concepts such as interest calculation, compound interest formulas, and trigonometric function applications. The construction utilizes GeoGebra commands and objects like LaTeX, VerticalText, PV, INSTRUCTIONS, QUESTION, R, r, i, numMonthsUnrounded, background, lblRate, Initialize, lblYaxis, TEXT, lblXaxis, lblR, futureValueOfPayments, futureValueOfPV, amountOwed, txtNumMonths. It is suitable for high school and above learners to understand financial mathematics concepts related to compound interest and repayment models.

GeoGebra Commands & Parameters

  1. LaTeX("\textbf{Instructions: }Use the sliders to change the value of the monthly payment and the value\\of the annual interest rate.") → INSTRUCTIONS
  2. LaTeX("\textbf{Question: } Juliette borrowed \(\$750\) at a rate of \(9.4\%\) per year compounded monthly. Every\\month, she pays back \(\$10\). The graph shows the outstanding balance of Juliette's loan at\\the end of each month. How does changing the amount of the monthly payment affect the\\time it takes Juliette to pay off her loan? How does changing the interest rate on the loan\\affect the time it takes to pay it off?") → QUESTION
  3. LaTeX((("\text{Annual interest rate = " * r) * "%}")) → lblRate
  4. VerticalText("Amount Owed in \$") → lblYaxis
  5. LaTeX((((("\text{" * QUESTION) * "\\") * INSTRUCTIONS) * "}")) → TEXT
  6. LaTeX("{\text{Time in Months}") → lblXaxis
  7. LaTeX((("\text{Monthly payment = \$" * R) * "}")) → lblR
  8. LaTeX((("\text{\fbox{Juliette's loan will be paid\\off in \(" * ceil(numMonthsUnrounded)) * "\) months.}}")) → txtNumMonths

AI Drawing Prompt Reference

Illustrate a loan repayment model with sliders for monthly payment and annual interest rate, and a graph showing the outstanding loan balance at the end of each month. The graph has months on the x-axis and dollars on the y-axis, with labels for the interest rate and monthly payment. Include text instructions and a question below the graph, asking how changes in payment amount and interest rate affect the repayment time.
The prompt above was compiled from the original drawing commands and is for reference only.