mortgage and amortizationbusinessss.pptx

it define mortgage and amortization, it also provide problem solving with complete solution. it has also worded problem that everyone would easily understand for sure. it contains formulas and also deriving

1. MORTGAGE AND AMORTIZATION LESSON 6:

2. LEARNING OUTCOMES: At the end of the lesson, you should be able to: Illustrate how interest is computed and applied on mortgage, amortization, services/utilities, deposits, and loans.

3. When purchasing real estate like houses or buildings, there is a way to make the purchase without having to pay for the whole cost of the property immediately. Such process is called MORTGAGE. A mortgage can be defined as an agreement by which a debtor pays the lender (usually a financial institution like a bank) for a certain property over a period of time. In most context, the term “mortgage” can also refer to the loan itself. Sometimes it is also called the PRINCIPAL AMOUNT OF THE LOAN. An important consideration in a mortgage is that, unlike in other loans or debts, an actual physical entity, which is the property itself, serves as the security or COLLATERAL for mortgage loans. If the borrower fails to pay for the loan, the collateral (which is the property) will be forfeited.

4. To further illustrate the concept of mortgage, consider this situation. Suppose you have saved ₱200,000 and you are planning to buy a house that costs ₱1,000,000. Since your savings is not enough to fully pay the house in cash, you can apply for a mortgage from a bank. Your savings can be used as down payment, and then you can pay the remaining balance to bank using the house as a collateral. The remaining balance, which is the amount loaned from the bank, is the mortgage. So in this situation, the mortgage (which we denote as M ) is the difference between the cost of the house and the down payment, that is; M= 1,000,000-800,000= 200,000

5. When the bank approves your mortgage loan, you can pay it back tom the bank on a periodic, installment basis. The amount that you need to pay based on the agreed upon schedule-for example, on a monthly basis-is called the AMORTIZATION . Amortization maybe thought of as an process of dividing the value of a loan by paying a certain fixed amount periodically. The payment schedule and the period during which you have fully pay the bank in order to acquire the property are based on the agreement between both parties. The banks earns by charging an interest on your loan. To determine the periodic payment that a b orrower needs to settle based on the mortgage and payment terms that a bank applies, we can use the formula that follows.

6. General Formula In Calculating The Periodic Payment For A Mortgage Let P be the principal amount, r be the interest rate, n be the number of payments per year, and t be the total number of years during which the mortgage will be paid. Then the periodic payment P M can be calculated using the following formula: P M =  

7. Observe that when we need to determine the monthly amortization for a mortgage, we just need to use n =12 in the given formula; hence, the formula will become: PM=   Also, take note that in this particular case, the interest is assumed to be compounded monthly. The next example demonstrate how this formula is used.

8. EXAMPLE 1: Determining the Monthly Payment for a Mortgage Suppose you want to buy a house that costs ₱1,000,000. You give a down payment of ₱200,000, and then you loan the remaining ₱800,000 from a bank. Your agreement with the bank is that you will pay for the mortgage on a monthly basis for 10 years and that the bank will change a 3% interest rate, compounded monthly, on your loan. Determine the amount of your monthly payment.

9. Solution and Answer: The following information were given in the problem: P = ₱800,000, t= 10 years, and r= 3. Since you will be paying on a monthly basis, we also have n= 12. The other given information (that is, the cost of the house and the amount of your down payment) are not necessary for solving the problem. We can use the general formula that was stated previously. So if we substitute the given values, we have;

10. P M= PM= PM= PM=   PM= PM= PM≈7,724.86   Therefore, you need to pay a monthly amortization of ₱7,724.86 for 10 years to fully pay the mortgage.

11. Now let us analyze the situation in example 1 further. In 10 years, you will have a total of 120 monthly payment; that is, n∙t = (12)(10)= 12. We have determined that the amount of each periodic or monthly payment is ₱7,724.86. So the total amount (which we denote as A) that you need to pay the bank is the product of the total number of monthly payment ( n∙t ) and the periodic payments (PM). In symbol, A= n ∙ t ∙ P M So the total amount that you will pay the bank is: A= (12)(10)(7,724.86)= 926,983.20 To get the total interest I that the bank charges on your mortgage, simply subtract the amount of the principal amount P from the total payment A. In symbol, I= A-P Hence, the total interest that you need to pay the bank is I= 926,983.20-800,000= 126,983.20

12. EXAMPLE 2: Problem Solving Involving Interest Applied on a Mortgage Amlong wants to purchase a car that costs ₱1,300,000. He will give a down payment of ₱300,000, and then he will loan the balance from the bank that charges a 7.5% interest rate, compounded monthly. He also agreed to pay the bank monthly for 5 years. How much is his monthly amortization? How much is the total interest in his loan?

13. Solution and Answer: Since the cost of the car is ₱1,300,000 and Amlong will give a down payment of ₱300,000, the principal amount P that he will borrow from the bank is: P= 1,300,000-300,000= 1,000,000 The following additional information were given in the problem: t= 5 years and r= 7.5%. Since he will be paying on a monthly basis, we also have n= 12.

14. 2 1. We can use the general formula for solving the monthly payment P M as shown below. P M= PM= PM= PM≈ 20,037.95   2 . To determine the total interest on his loan, we need to solve first for the total amount A of his payments; that is, A= n ∙ t ∙ PM A= (12)(5)(20,037.95) A= 1,202,277 Then solve for the total interest I as follows: I= A-P I= 1,202,277-1,000,000 I= 202,277 Thus, the total interest on his loan is ₱202,277 Therefore, Amlong needs to pay the bank a monthly amortization of ₱20,037.95 for 5 years

15. EXAMPLE 2: Problem Solving Involving Interest Applied on a Mortgage Suppose you are planning to apply for a housing loan. The lender offers different interest rates that reflects the difference in terms of the risk of the shortest-term and longer-term loans. The following are the options that were given to you: Option A: The mortgage will be paid on a monthly basis for 15 years at an interest rate of 6.25%, compounded monthly Option B: The mortgage will be paid on a monthly basis for 30 years at an interest rate of 6.75%b, compounded monthly

16. If you plan to borrow ₱2,400,000, how much will be your monthly amortization in each option? 2. Explain the advantages and disadvantages of each option.

17. Solution and Answer: In both options, the principal amount P is ₱2,400,000 and the payment will be on a monthly basis, which means that n= 12. For option A, the following information were given: t= 15 years and r= 6.25%. So we have: P M= PM=   PM= PM≈ 20,565.07   Thus, in Option A, the monthly amortization is approximately ₱20,565.07 for 15 years

18. For Option B, the following information were given: t= 30 years and r= 6.75%. Thus we have: P M= PM=   PM= PM≈ 15,518.52   Therefore, in Option B, the monthly amortization is approximate ₱15,518.52 for 30 years

19. 2. If we will compare the results in item (1), we can say that you will pay a lower monthly amortization in option B (which is a longer-term loan) than in option A (which is a shorter-term loan). However, we also need to compare the total interest that you need to pay the bank. For option A, the total payment and the total interest can be computed as follows: A= n ∙ t ∙ P M A≈ (12)(15)(20,565.07) A≈ 3,701,712.60 I= A-P I≈ (12)(10)(2,400,000) I≈1,301,712.60 Therefore, the total interest in option A is ₱1,301,712.60

20. For option B, the total payment and the total interest can be computed as follows; A= n ∙ t ∙ P M A≈ (12)(30)(15,518.52) A ≈ 5,586,667.20 I= A-P l≈ 5586,667.20-2,400,000 l ≈ 3,186,667.20 So the total interest in Option B is ₱3,186,667.20

21. Notice that although option B has a lower monthly amortization, the total interest that you need to pay is much higher than that in option A. Generally, shorter-term loans (like option A) is better than a longer-time loans (like option B) of you want to pay a lower total interest. But the downside for shorter-term loans is that the monthly amortization is usually higher. In the end, the payment terms that will more advantageous to you will depend on your capacity to pay.