Financial Algebra© Cengage/South-Western Slide 11

4-3

LOAN CALCULATIONS AND REGRESSION

Calculate the present value of a single deposit investment.

Calculate the present value of a periodic deposit investment.

OBJECTIVES

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monthly payment calculator natural logarithm linear regression equation quadratic regression equation cubic function cubic regression equation

Key Terms

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Hannah is taking out a 4.3% loan to purchase an $18,000 car. The length of the loan is 8 years. How much will she pay in interest?

Example 1Example 1

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Exponential Bases and Natural LogarithmsExponential Bases and Natural LogarithmsExponential Bases and Natural LogarithmsExponential Bases and Natural Logarithms

xey

yx ln

xe130 :Solve

130 lnx 94.

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Loan Length FormulaLoan Length FormulaLoan Length FormulaLoan Length Formula

12112

12

r

rpM

pM

t ln

ln ln

M = monthly payment p = principal r = interest rate t = number of years

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Example 2Example 2

Claude wants to borrow $25,000 to purchase a car. After looking at his monthly budget, he realizes that all he can afford to pay per month is $300. The bank is offering a 5.9% loan. What would need to be the length of his loan be so that he can stay within his budget?

Financial Algebra© Cengage Learning/South-Western Slide 77

This lesson opened with a discussion about a $100,000 loan with an APR of 7.5% taken out in January 2010 for a period of 15 years. Examine the table of decreasing loan balances over the 15-year period. Use regression to determine a curve of best fit for this data.

EXAMPLE 3EXAMPLE 3

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Use the linear, quadratic, and cubic regression equations determined in Example 3 to compare the computed loan balances when x = 2 with the loan balance amount given in the chart for 2011.

CHECK YOUR UNDERSTANDING