3 4 LOAN CALCULATIONS AND REGRESSION OBJECTIVES Determine

3 -4 LOAN CALCULATIONS AND REGRESSION OBJECTIVES Determine the interest on a loan given the principal, time, and APR. Use the logarithmic loan length formula to determine the term of a loan. Use regression to fond the curve of best fit using data from a loan table. Slide 1

Key Terms • • monthly payment calculator loan length formula cubic function cubic regression equation Slide 2

How can you calculate and model loan computations? • How does a loan payment work? • Which of the following change monthly and which remain the same each month? – Monthly payments – Monthly contribution to principal – Monthly contribution to finance charges Slide 3

How can you calculate and model loan computations? (Continued) Slide 4

Example 1 Determine the total interest owed on a 5 -year $10, 000 loan at 6% APR. Slide 5

Example 1 Determine the total interest owed on a 5 -year $10, 000 loan at 6% APR. Slide 6

Example 1 Determine the total interest owed on a 5 -year $10, 000 loan at 6% APR. Slide 7

Example 1 Determine the total interest owed on a 5 -year $10, 000 loan at 6% APR. Slide 8

Example 1 Determine the total interest owed on a 5 -year $10, 000 loan at 6% APR. Slide 9

Example 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? M = Monthly Payment P = Principal R = rate (decimal) Slide 10

Example 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? Slide 11

Example 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? Slide 12

Example 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? Try with Calculator Slide 13

Example 3 John does not have a very good credit rating. In January of 2016, he found a lending institution that was willing to loan him $100, 000 for 15 years at a higher than normal interest rate of 7. 5% because of his poor credit rating. Examine the table of decreasing loan balances over the 15 -year period. Use regression to determine a curve of best fit for this data. Slide 14

Example 3 Slide 15