Section 4.5 (Amoritization Tables)

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1 Math 34: Fall 2014 Section 4.5 (Amoritization Tables) Amortization Tables help us understand how interests affects annuities when a loan is being paid down. They can help us understand why when Ferguson cut the term of his mortgage in half, his payments didn t just double. How to Set up an Amortization Table One row for each payment of the loan (sometimes in HW you ll only be asked to do the first few rows) There are columns for Payment Number, Payment Amount, Interest Amount, Principal Amount and Remaining Balance. Payment Amounts will always be the same in an annuity Interest Amount and Principal Amount are really amount of the payment that goes toward interest and amount of the payment that goes toward paying down the principal, but those names are too long Interest Amount is found using Interest = P RT where the P is the remaining balance from the previous row Principal Amount Some of your payment goes toward interest, the rest goes toward paying down the principal so... Principal Amount = Payment - Interest Amount Remaining Balance You are paying off the principal amount, so your balance decreases by that amount Remaining Balance = (Rem. Balance prev. row) - (Principal Amt. this row) 1

2 Example: Alycia needs to borrow money for some plumbing repairs on her home. The repairs cost $2, , and she finds that her local bank will loan her the money for one year at 7.44% interests (compounded monthly). Make an Amortization Table For all 12 Months of this loan Using a /12 = , Alycia and her bank determine that her monthly payments will be $2, / = , which they round to $200 a month , , , , , , Things to notice from the Amortization Table The payment amount is the same each month, but the split between interest and principal changes As time goes on, your balance gets paid down, this means the interest you pay is less as time goes on. We use simple interest (rather than compound interest) since we wipe out (pay off) the interest each onto, there isn t any interest to compound on. 2

3 Example: Let s look at the same example, but if Alycia had decided to take a 3 year loan for the $2, at the same 7.44% interest. Using a /12 = , Alycia and her bank determine that her monthly payments will be $2, / = , which they round to $71.67 a month , , , , , , , , , , , , , , , , , , , , ,

4 Note that the total paid for the 1 year loan was = $2, 400 So Alycia paid less than $100 in interest. The total paid for the 3 year loan was = $2, , so Alycia paid $ in interest. The interest is the same in month 1 for both loans. But since Alycia pays more in month 1 with the shorter loan, more money comes off the principal, so the interest she s paying in month 2 is lower with the shorter loan. Remaining Balance of an Amortized Loan At any point in the term of an Amortized loan, the amount owed is equal to the present value of the remaining payments. Example Consider Alycia borrowing $2, at 7.44% interests for 1 year. Use the above formula to calculate Alycia s remaining balance after 7 months. Does your answer agree with the table? Consolidation and Refinancing Refinancing means paying off an existing debt by taking out a new loan, borrowing the money needed to pay off the old one. Consolidating loans means replacing several loans with a new loan. To answer questions about consolidating and/or refinancing: You will often need to know the total amount(s) that remain on the old loan(s). This/these can be found using the remaining balance formula. The total amount(s) remaining on the old loan will be the Present Value of the new loan (you are borrowing the amount of money you need to pay off the old loans). You can use what you know from previous sections to determine monthly payments, total amount paid, total interest paid etc. The questions may end with you being asked to compare the old loan(s) to the new loan. 4

5 1. Aaron has 9 years left on a business loan at 11.5%, on which his quarterly payments are $3, 200. Because interest rates have dropped and Arron s credit rating has improved, he now equalities for a loan at 8.7% interest. Assume he refinances his debt to a new 9 year loan where he will make monthly payments. How much in total interest will he save? 2. Alejandro has the following monthly obligations: A mortgage payment of $680 for the next 170 months at $4.2%, payments on a car loan of $ for the next 30 months at 5.9% and student loan payments of $ for the next 93 months at 4.66%. A finance company suggests that Alejandro consolidate his loans and lower his monthly payments. They suggest he consolidate his mortgage, car loan, and student loans and take out a new 30 year mortgage at 4.25%. (a) What would Alejandro s new monthly payments be? How do these compare to his old monthly payments? (b) How much (in total) would this consolidating save Alejandro? Amount Alejandro Owes on Mortgage: a /12 = P V = = $87, Amount Alejandro Owes on Car: a /12 = P V = = $6, Amount Alejandro Owes on Student Loans: a /12 = P V = = $24, (Optional) Anastasia has a 20 year mortgage at 3 3 % interest where $140, was borrowed. (a) Find the monthly payments (b) Fill out the first 3 months of an Amortization Table for this loan. (c) How much will Anastasia owe on her mortgage after 5 years? (d) (Optional) How much will Anastasia owe on her mortgage after 10 years? (e) (Optional) How much will Anastasia owe on her mortgage after 15 years? 4. (Optional) Allie has a loan with 11 years left, her monthly payments are $198.50, and the interest rate is 8.4%. (a) How much does Allie owe now? (b) If Allie has the option to refinance with a new 10 year loan at 8.25%, how much would her monthly payments be? (c) With the new 10 year loan, how much would Allie save in interest? 5