M110 SECTION 9.5 AMORTIZATION DAY 1 So you found your dream home. Terrific! Only 30 years of payments and it will be all yours! You took out a loan from the bank and now you must repay that loan, plus the accumulated interest, in monthly payments. The process of paying off a loan (plus interest) by making a series of regular, equal payments is called amortization. EXAMPLE You have purchased a new boat for $15,000. You make a $5,000 down payment and borrow the rest of the money from the bank. You agree to pay back the loan plus interest in 4 years at 18% annual interest. The banker’s point of view Your point of view He uses the compound interest formula You are thinking this is like a sinking fund -- to calculate the future value of the loan. that is, making a series of regular payments to “save” for the loan plus interest. ntnr1PA+= ÷−+⋅=nr1nr1RAnt Since both the above equations are equal to A, we can set them equal to each other: ÷−+⋅=+nrnr1 R nr1Pntnt1 FORMULA FOR R, THE REGULAR MONTHLY PAYMENT We will use this formula to find R, the regular monthly payment, to pay off the loan amount ($10,000) plus interest over the next 4 years at 18% annual interest. Find the payment for the above example. ÷−+⋅=+nrnr1 R nr1Pntnt1 (ALWAYS ROUND THE PAYMENT UP TO NEXT HIGHER CENT!) R = ? P = _______________ r = _________ n = _________ t = _________Now, let us look at the first few months of payments. There are a few things to keep in mind: 1. Your payment is paying off BOTH the loan amount AND THE INTEREST 2. You are borrowing A LOT of money ($10,000), so at the start of repaying the loan you owe interest on the full amount. 3. As the principal is reduced each payments pays more toward principal and less toward interest. This list showing payment-by-payment how much is going to principal and interest is called an amortization schedule or table. Payment Number Amount of Payment Interest Applied toward reducing the Principal (Balance) Balance $ 10,000 1 $293.75 2 $293.75 3 $293.75 4 $293.75EXAMPLE To expand your business, you need a loan of $5,000. Your bank loans you the money at 12% annual interest rate, which you agree to pay back in 3 equal monthly installments. Find the monthly payment and construct an amortization schedule for the entire loan. ÷−+⋅=+nrnr1 R nr1Pntnt1 Payment Number Amount of Payment Interest Applied toward reducing the Principal (Balance) Balance 1 2 3 Be sure to adjust the 3rd and Final Payment so to kill the loan perfectly!EXAMPLE You have purchased a new home for $145,000. You make a $25,000 down payment and borrow the rest of the money from the bank. The bank offers you a 30-year mortgage at an annual interest rate of 7%. Find the monthly payment and construct an amortization schedule for the first 3 payments. ÷−+⋅=+nrnr1 R nr1Pntnt1 Payment Number Amount of Payment Interest Applied toward reducing the Principal (Balance) Balance $ 120,000 1 2 3EXAMPLE You buy a home for $297, 000. You put 25% down and secure a loan for the remainder for 25 years at an annual interest rate of 7%. a. What is the amount of your mortgage? b. What is your monthly mortgage payment? c. What is the total of the payments over the life of the loan? d. How much interest did you pay over the 25 years? (Shocking, isn’t it?) e. In the end, how much did you pay for the