financial algebra © cengage/south-western slide 1 4-3 loan calculations and regression calculate...
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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
Financial Algebra© Cengage Learning/South-Western Slide 22
monthly payment calculator natural logarithm linear regression equation quadratic regression equation cubic function cubic regression equation
Key Terms
Financial Algebra© Cengage Learning/South-Western Slide 33
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
Financial Algebra© Cengage Learning/South-Western Slide 44
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.
Financial Algebra© Cengage Learning/South-Western Slide 55
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
Financial Algebra© Cengage Learning/South-Western Slide 66
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
Financial Algebra© Cengage Learning/South-Western Slide 88
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