LESSON PLAN FOR GRADE 11

LESSON PLAN School                          : Senior High School of TAU Subject                         : Bussiness Mathematics Class/Chapter              : 11 / 3 Subject Matter             : Mortgages, Amortisation & Sinking Fund Time allocation            : 60-240 minutes

Focus Standards :

1.      Discuss mortgages, amortisation & sinking fund.

2.      Analyze, practic and solve the problem about mortgages, amortisation & sinking fund.

3.      Understand all material about mortgages, amortisation & sinking fund.

Resources material

·         Mortgages, Amortisation & Sinking Fund (attached)

Lesson Target

·         After following the instructional student can :

1.      Comprehend what a mortgages is.

2.      Compute for the down payment on a mortgages and the amount of the mortgages loan.

3.      Determine how payment is applied to interest and principal, and determine the balance of the loan after each payment

4.      Prepare an amortization table.

5.      Solve problem involving mortgages.

6.      Calculate the periodic payment and the original amount of the loan in an amortization problem.

7.      Construct the amortization schedule.

8.      Compute the outstanding obligation by prospective and retrospective methods.

9.      Determine the number of payments and the amount of the final payment in an amortization with an irregular payments.

10.  Calculate the final amount and the periodic deposit in a sinking fund problem.

11.  Sut-up the sinking fund table.

12.  Exhibit flexibility by using both the table and calculator in computation.

Teaching Method

Approach  :  Scientific Approach

Model        :  Cooperative

Method     :  Group discussion, Numbered Heads Together

Guiding Question(s) :

1.      What is the meaning of mortgages, amortisation & sinking fund?

2.      What the relation betweet mortgages, amortisation & sinking fund?

3.      How to calculate mortgages, amortisation & sinking fund?

4.      How to solve practical applications involving mortgages, amortisation & sinking fund?

Vocabulary

Academic Vocabulary : 1.      Mortgages 2.      Down payment 3.      Amortization 4.      Amortization schedule 5.      Prospective method 6.      Retrospective method 7.      Sinking fund 8.      Sinking fund table 9.      Book value

Instructional Strategies for Academic Vocabulary :        Introduce academic vocabulary with student-friendly definitions.        Model how to use academic vocabulary in discussion.        Discuss the meaning of an academic vocabulary word in a business and mathematical context.        Justify responses and critique the reasoning of others using academic vocabulary        Cite examples to represent academic vocabulary.        Write or use literacy strategies involving academic vocabulary.

INSTRUCTIONAL PLAN

Lesson Purpose and Student Outcomes : Student will be able to understand and solve the problem about mortgages, amortisation & sinking fund.

Introduction Activity

-          The teacher gives opening and greeting.

-          The teacher asks them to pray together.

-          The teacher checks students attendance and asks condition of the students.

-          The teacher gives a review of the previous material (ie simple interest).

-     The teacher provide motivation and appreception so the students will be more interested in learning.

Introduction to the Lesson : The teacher shows a video about mortgages and give ample time to the student to analyze the video. The video is about what the meaning of mortgages, the illustration and how to calculate mortgages.
Then after the activity, teacher will give explanation about mortgages to make the student more understand. The teacher will say that :

“Mortgages is debt instruments by assigning mortgages to property and borrowers to lenders as security against their obligations.”

• Then the teacher will illustrates process of mortgages. The illustration is relaled with when we want to buy a house and we don’t have maney. So we need mortgage loans.
• Teacher explain the different of mortgages and loans.

 Mortgages or mortgages are:
A debt instrument by assigning mortgages to property and borrowers to a lender as security against its obligations.
In this case, the borrower can still use or utilize the property. The mortgage rights on the property fall once the obligation is paid in full.

Loans or loans are:
The relationship between the lender's money (Creditor) and the borrower of money (Debtor).
The borrower not only returns the money with the amount initially borrowed but the borrower must also refund the additional cost (interest).

• Then teacher will ask the student who can repeat the different of mortgages and loans for make sure they listening.
• For the student that can answer correctly teacher will give an extra point.
• After the activity teacher explain how to calculate mortgages with this case :

1.      You want to buy a secondhand car worth P312500 and the seller requires a 20% down payment. 

       How much the mortgage loan?

Solution : Purchase price – (Prurchase price x Down payment %)

                     Mortgage loan    = P312500 – (P312500 x 20%)

                                                    = P312500 – P62500

                                                    = P250000 

2.      You wish to buy a house w ith price P1.146.000 and the seller require a 25% down payment. 

       How much the mortgage loan?

Solution : Purchase price – (Prurchase price x Down payment %)

               Mortgage Loan    = P1.146.000 – (P1.146.000 x 25%)

                                              = P1.146.000 – P286.500

                                              = P859.500

3.      You wish to buy a land with price P1.908.000 and the seller require a 15% down payment. 

       How much the mortgage loan?

Solution : Purchase price – (Prurchase price x Down payment %)

               Mortgage Loan    = P1.908.000 – (P1.908.000 x 15%)

                                              = P1.908.000 – P286.200

                                              = P1.621.800

Next Material : Monthly Payment

Mmonthly Payment Formula :

	P =      L[c(1 + c)n] [(1 + c)n - 1]

 

•  Before we calculate the monthly payment, we must to know the number of payment. For make us easier to understan and to calculate the payment we will make amortization table. Amortizationj table is the schedule that showing the installment payment for the period of payment.
• So in our first example (give simbol like circle or check in the first example) assume that you have to make one payment per month for 30 years. It means that you have to make 360 (12x30 years) monthly payment in term of the loan. And the bank will charge 5% annually.
•  Lets discuss

The number of payment = P250.000/360

                                         = P694.44

We devide 5%                 = 5% / 12

                                         = 0,416 %

Monthly payment             = (0,00416)(P250.000) x (1+0,00416)³⁶⁰

                                                                         (1+0,00416)³⁶⁰ – 1

                                                     = P1.342,05

So you have to pay P1324,05 for your monthly payment.

Monthly Amortization Schedule

Payment	Amount	Principal	Interest	Balance
1	1.342,05	300.39	1046.67	249699.61
2	1.342,05	301.64	1040.42	249397.97
3	1.342,05	302.90	1039.16	249095.08
4	1.342,05	304.16	1037.90	248790.92
5	1.342,05	305.43	1036.63	248485.49
etc
360	1.342,05	1336.49	5.57	0
Totals	483139.46	250000.00	233139.49

Assignment :

1. You wish to buy a house with price P1.146.000 and the seller require a 25% down payment. How much the mortgage loan? And you have to make payment every month in 20 years, the bank will charge 10% annually. Please count the month payment and make the monthly amortization schedule.

Amortization and Sinking Fund

Instructional material :

• The teacher make relation about Mortgages material and Amortization material.
•  The teacher explain the meaning of amortization and Sinking Fund.

“Decrease or the value of an intangible asset gradually over a period of time in each accounting period.”

·         The formula for amortization  is :

A = Principal

R = Periodic Payment

i = interest per period

n = Total Number of Payment Periods

Example :

1.      An obligation of P21,000 with interest of 8% compounded semi-annually must be paid at the end of every 6 month for 4 years.

a.       Find the size of periodic payment.

b.      Find the remaining liability just after making the 5^th payment.

c.       Prepare the amortization table.

Solution :

A = P21,000                   t = 4 years

j = 8%                             i = 0.04

m = 2                               n = 8

c.       Amortization table

Period	Balance	Payment	Interest Paid	Payment For Principal
1	P21,000.00	3,119.08	840.00	P2,279.00
2	18,720.92	3,119.08	748.84	2,370.24
3	16,350.68	3,119.08	654.03	2,465.05
4	13,885.63	3,119.08	555.43	2,563.65
5	11,321.78	3,119.08	452.88	2,666.20
6	8,655.78	3,119.08	346.23	2,772.85
7	5,882.93	3,119.08	235.72	2,883.76
8	2,999.16	3,119.08	119.97	2,999.11
Total		P24,952.64	P3,953.10	P21,000.00

Assignment

           Make one case or problem about amortization, then collect to the teacher and the teacher will the teacher will randomize the problem and give to the other students, and the students who got the problem must answer the questions it receives.

Sinking Fund

Sinking fund refers to a fund created by making periodic deposit to anticipate the need of paying a large amount of money at some future dates.

A sinking fund schedule illustrates how thr fund accumulates every payment period, and to determine the amount in the fund at any given time, the following geometeric progression formulas for ordinary annuity are used.

Example :

1.      A fund is created by making equal monthlydeposits of P3,000 at 9% converted monthly.

a.       Determine the sum after half year.

b.      What is the amount in the fund after the 4^th deposit?

c.       Costruct the sinking fund schedule for a 6-monthy period.

Given :

R = P3,000

j = 9%

m = 12

Solution :

c)      Sinking fund Schedule

No of Payment	Periodic Deposit	Interest in Fund	Increase in Fund	Amount of Fund
1	P3,000	0	P3000.00	P3000
2	P3,000	22.50	3,022.50	6,022.50
3	P3,000	45.17	3,045.17	9,067.67
4	P3,000	68.01	3,068.01	12,135.68
5	P3,000	91.02	3,091.02	15,226.70
6	P3,000	114.20	3,114.20	18,340.90

Assessment

1.      A fund is being created by paying P2500 at the end of each year at 10.25% compounded annually foe 4 years.

a.       How much money is in the fund just after the 3^rd deposit?

b.      Construct a sinking fund Schedule foe 4 years.

2.      What monthly payment into a sinking fund at 8% compounded semi-annually will be needed to raise P50,200 at the end of 2 years and 6 months?