Installment Loans. Lecture 23 Section Robb T. Koether. Hampden-Sydney College. Mon, Mar 23, 2015

Transcription

1 Installment Loans Lecture 23 Section 10.4 Robb T. Koether Hampden-Sydney College Mon, Mar 23, 2015 Robb T. Koether (Hampden-Sydney College) Installment Loans Mon, Mar 23, / 12

2 1 Installment Loans 2 Assignment Robb T. Koether (Hampden-Sydney College) Installment Loans Mon, Mar 23, / 12

3 Outline 1 Installment Loans 2 Assignment Robb T. Koether (Hampden-Sydney College) Installment Loans Mon, Mar 23, / 12

4 Installment Loans Definition (Installment Loan) With an installment loan, the borrower pays back the loan through regular payments, usually monthly. Each month, The interest rate is applied to the outstanding balance from the previous month. The interest is added to the outstanding balance. And the payment is subtracted from the outstanding balance, producing the balance to be carried over to the next month. In order to pay the loan off, the monthly payment must be greater than the monthly interest. The greater the difference, the faster the loan is paid off. Robb T. Koether (Hampden-Sydney College) Installment Loans Mon, Mar 23, / 12

5 Installment Loans The formula for the payment M is Pr(1 + r)n M = (1 + r) n 1 Pr = 1 (1 + r) n, where P is the principal (amount borrowed), r is the interest rate per period, and n is the number of payments. Payments are usually monthly, but they do not need to be. Robb T. Koether (Hampden-Sydney College) Installment Loans Mon, Mar 23, / 12

6 $455 is borrowed at 20% for 3 years, with payments made annually. Find the annual payment. Trace the balance over the three years as interest is applied and the payments are made. Robb T. Koether (Hampden-Sydney College) Installment Loans Mon, Mar 23, / 12

7 The payment is M = Pr 1 (1 + r) n Robb T. Koether (Hampden-Sydney College) Installment Loans Mon, Mar 23, / 12

8 The payment is M = Pr 1 (1 + r) n = (455)(.20) 1 (1.20) 3 Robb T. Koether (Hampden-Sydney College) Installment Loans Mon, Mar 23, / 12

9 The payment is M = Pr 1 (1 + r) n = (455)(.20) 1 (1.20) 3 = $216. Robb T. Koether (Hampden-Sydney College) Installment Loans Mon, Mar 23, / 12

10 Starting Ending Year Balance Interest Total Payment Balance 1 $455 $91 $546 $216 $330 Robb T. Koether (Hampden-Sydney College) Installment Loans Mon, Mar 23, / 12

11 Starting Ending Year Balance Interest Total Payment Balance 1 $455 $91 $546 $216 $330 2 $330 $66 $396 $216 $180 Robb T. Koether (Hampden-Sydney College) Installment Loans Mon, Mar 23, / 12

12 Starting Ending Year Balance Interest Total Payment Balance 1 $455 $91 $546 $216 $330 2 $330 $66 $396 $216 $180 3 $180 $36 $216 $216 $0 Robb T. Koether (Hampden-Sydney College) Installment Loans Mon, Mar 23, / 12

13 Now consider a $10,000 loan at 4% for 10 years, paid in annual payments. Robb T. Koether (Hampden-Sydney College) Installment Loans Mon, Mar 23, / 12

14 Now consider a $10,000 loan at 4% for 10 years, paid in annual payments. The annual payment is M = (10000)(0.04) 1 (1.04) = = Robb T. Koether (Hampden-Sydney College) Installment Loans Mon, Mar 23, / 12

15 Starting Ending Year Balance Interest Payment Balance 1 $10,00000 $ $1, $9, Robb T. Koether (Hampden-Sydney College) Installment Loans Mon, Mar 23, / 12

16 Starting Ending Year Balance Interest Payment Balance 1 $10,00000 $ $1, $9, $9, $ $1, $8, Robb T. Koether (Hampden-Sydney College) Installment Loans Mon, Mar 23, / 12

17 Starting Ending Year Balance Interest Payment Balance 1 $10,00000 $ $1, $9, $9, $ $1, $8, $8, $ $1, $7, Robb T. Koether (Hampden-Sydney College) Installment Loans Mon, Mar 23, / 12

18 Starting Ending Year Balance Interest Payment Balance 1 $10,00000 $ $1, $9, $9, $ $1, $8, $8, $ $1, $7, $7, $ $1, $6, Robb T. Koether (Hampden-Sydney College) Installment Loans Mon, Mar 23, / 12

19 Starting Ending Year Balance Interest Payment Balance 1 $10,00000 $ $1, $9, $9, $ $1, $8, $8, $ $1, $7, $7, $ $1, $6, $6, $ $1, $5, Robb T. Koether (Hampden-Sydney College) Installment Loans Mon, Mar 23, / 12

20 Starting Ending Year Balance Interest Payment Balance 1 $10,00000 $ $1, $9, $9, $ $1, $8, $8, $ $1, $7, $7, $ $1, $6, $6, $ $1, $5, $5, $ $1, $4, Robb T. Koether (Hampden-Sydney College) Installment Loans Mon, Mar 23, / 12

21 Starting Ending Year Balance Interest Payment Balance 1 $10,00000 $ $1, $9, $9, $ $1, $8, $8, $ $1, $7, $7, $ $1, $6, $6, $ $1, $5, $5, $ $1, $4, $4, $ $1, $3, Robb T. Koether (Hampden-Sydney College) Installment Loans Mon, Mar 23, / 12

22 Starting Ending Year Balance Interest Payment Balance 1 $10,00000 $ $1, $9, $9, $ $1, $8, $8, $ $1, $7, $7, $ $1, $6, $6, $ $1, $5, $5, $ $1, $4, $4, $ $1, $3, $3, $ $1, $2, Robb T. Koether (Hampden-Sydney College) Installment Loans Mon, Mar 23, / 12

23 Starting Ending Year Balance Interest Payment Balance 1 $10,00000 $ $1, $9, $9, $ $1, $8, $8, $ $1, $7, $7, $ $1, $6, $6, $ $1, $5, $5, $ $1, $4, $4, $ $1, $3, $3, $ $1, $2, $2, $93.01 $1, $1, Robb T. Koether (Hampden-Sydney College) Installment Loans Mon, Mar 23, / 12

24 Starting Ending Year Balance Interest Payment Balance 1 $10,00000 $ $1, $9, $9, $ $1, $8, $8, $ $1, $7, $7, $ $1, $6, $6, $ $1, $5, $5, $ $1, $4, $4, $ $1, $3, $3, $ $1, $2, $2, $93.01 $1, $1, $1, $47.42 $1, $ 0.02 Robb T. Koether (Hampden-Sydney College) Installment Loans Mon, Mar 23, / 12

25 Example (Financing a Car) You would like to purchase a new car priced at $25,000. You can put $5,000 down and finance the rest at 6% for 60 months. Find The monthly payment. The total amount of interest paid. Robb T. Koether (Hampden-Sydney College) Installment Loans Mon, Mar 23, / 12

26 Example (Home Mortgage) You would like to purchase a home for $300,000. You can put $60,000 down and finance the rest at 4% for 30 years or at 3% for 15 years. Find The monthly payment for each choice. The total amount of interest paid for each choice. Robb T. Koether (Hampden-Sydney College) Installment Loans Mon, Mar 23, / 12

27 Outline 1 Installment Loans 2 Assignment Robb T. Koether (Hampden-Sydney College) Installment Loans Mon, Mar 23, / 12

28 Assignment Assignment Chapter 10: Exercises 51, 52, 53, 55, 56, 58. A person borrows $25,220 at 5% for 3 years, making 3 annual payments. Calculate the annual payment. Trace the balance through the two years as the interest is added and the payments are subtracted. The balance at the end of 3 years should be $0. Robb T. Koether (Hampden-Sydney College) Installment Loans Mon, Mar 23, / 12