Gen Math 11 Q2 Week 1 - Compound interest PDF

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Compound interest...

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11 GENERAL MATHEMATICS Quarter 2 – Module 1 Simple and Compound Interest

JULIE FE E. FERRAREN

Development Team of the Module Writers:

Julie Fe E. Ferraren

Editors: Assigned Editors in AP for each grade level Reviewers:

Dr. Jephone P. Yorong

Illustrator:

Edgardo P. Jamilar, Jr.

Layout Artist:

Peter A. Alavanza

Management Team: Felix Romy A. Triambulo, CESO VI Dr. Aurelio A. Santisas Dr. Ella Grace M. Tagupa Dr. Jephone P. Yorong Wevina Quizo School Head

Learning Objective/s This lesson will help you in developing your knowledge and skills in key concepts of rational functions upon following the instructions and doing the activities on the succeeding pages. After going through this module, you are expected to: • • •

Illustrates simple and compound interest Distinguishes between simple and compound interest. Computes simple interest

Lesson Proper Activity 1 Orly invested P100 000.00 to an account that pays a simple interest of 3% annually. Find the interest earned after 2 years. Complete the table below. At the end of 1 year 2 years 3 years

Principal

100, 000 100, 000 100, 000

Accumulated interest at 3% 3, 000

Amount due 103, 000

Simple Interest Simple Interest is charge only on the loan amount called principal. Simple Interest is calculated by multiplying the principal by the rate of interest by the number of payment periods in a year. I = Prt 𝐼 a. 𝑃 = 𝑟𝑡

b. 𝑟 =

𝐼 𝑃𝑡

c. 𝑡 =

𝐼 𝑃𝑟

Where I = interest, P = Principal, r=rate of interest, and t = time or term in years or fraction of a year To find the maturity value, Maturity Value or (Amount or Balance) A = P + I or A = P + Prt or A = P(I +rt) A = Maturity value

P = Principal

I = Interest

Activity 2 Arthur borrows P40 000.00 at 6% simple interest for a period of 1 year. At the end of one year, how much must he pay? ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ If Arthur did not pay back the loan or the interest by the end of the first year and he wanted to continue the loan for another year at the same rate, the he would owe P40 000.00 plus the interest incurred during the first year of loan. How much must he pay at the end of the second year? ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ If the same thing happens, that is Arthur was not able to pay back the loan or the interest by the end of the second year. The lender gave him another year under the condition, how must he pay at the end of the third year. _________________________________________ ______________________________________________________________ ______________________________________________________________ The problem in Activity 3 is an example of compound interest. For example, P40 000.00 was loaned for a period of 3 years with interest compounded annually. Bank pay compound interest on the savings accounts. When the interest due at the end of a certain period is added to the principal and that sum earns interest for the next period, the interest paid is called the compound interest. Compound interest is the procedure in which interest is periodically calculated and added to principal. The time interval between succeeding interest calculations is called the conversion period or compounding period or interval period. The compound frequency (or conversion frequency) is the number of compoundings that take place in a year. The common compounding or conversion frequencies and the corresponding compounding or conversion periods encountered are listed in Table below. Compounding Frequencies and Periods Compounding or No. of compoundings or Compounding or conversion frequency conversions per year conversion periods Annual 1 1 year Semiannual 2 6 months Quarterly 4 3 months Bimonthly 6 2 months Monthly 12 1 month

The example in the Activity can be answered as shown in the following table: At the end of Principal at Interest Amount the start of (at the end of the the year year)

First year

P40 000.00

Second year

P42 400.00

Third year

P44 944

40 000 X 0.06 X 1 = P2 400.00 42 400 X 0.06 X 1 = P2 544.00 44 944 X 0.06 X 1 = P2 696.64

P40 000 + P2 400 = P42 400.00 P42 400 + P2 544 = P44 944.00 P44 944 + P2 696.64 = P47 640.64

The amount (A) at the end of the year is equal to the sum of the principal (P) and the interest (Pr) for that year. In symbols,

A = P + Pr = P (1+r) In general, when interest is compounded annually for n years, the amount (or future value) A is

A = P (1+r)t

Analysis Write SI if the given problem involves Simple Interest and CI if the given problem involves Compound Interest. ___1. Find the interest on P28, 700 at 7.3% from March 14, 2016 to August 16, 2016 using ordinary interest using actual time. ___2. If Adam borrowed P300, 000 from a commercial bank charging 16% simple interest, how much would she pay at the end of 3 years. ___3. Alexander borrows P47, 400 with interest at 18% compounded quarterly. How much should he pay to the creditor after 3 years to pay off his debt? ___4. Four years ago, Nathan invested P23 900 compounded bimonthly at 12%. How much is his money now? ___5. John borrowed P23 700 and after 3 years, paid back the loan with 8% interest. How much was the interest paid.

Application Example 1. To buy school supplies for the coming school year, you get a summer job at a resort. Suppose you save P4 200 of your salary and deposit it into an account for simple interest. After 9 months, the balance is P4, 263.00. What is the annual interest rate?

Solution: 𝐼 where P = P4 𝑃𝑡 9 3 or 4 year, and 12

Use the formula 𝑟 =

200.00

T = 9 months or I = P4 236.00 –P4 200.00 = P63.00 63 𝑟= 3 = 0.02 𝑜𝑟 2% (4 200)( ) 4

Evaluation Given Problem: Teresa borrowed P120 000.00 from her uncle and agreed to pay annual interest rate.

1. Refer to the given problem, if Teresa agreed to pay an 8% annual interest rate, calculate the amount of interest she must pay if the loan period is 1 year. a. P9 600.00 c. P7 200.00 b. P14 400.00 d. P8 000.00 2. Refer to the given problem, if Teresa agreed to pay an 8% annual interest rate, calculate the amount of interest she must pay if the loan period is 18 months. a. P9 600.00 c. P7 200.00 b. P14 400.00 d. P8 000.00 3. Refer to the given problem, if Teresa agreed to pay an 8% annual interest rate, calculate the amount of interest she must pay if the loan period is 9 months. a. P9 600.00 c. P7 200.00 b. P14 400.00 d. P8 000.00 4. Refer to the given problem, if Teresa agreed to pay an 10% annual interest rate, calculate the amount of interest she must pay if the loan period is 1 year. a. P9 600.00 c. P7 200.00 b. P14 400.00 d. P12 000.00 5. Refer to the given problem, if Teresa agreed to pay an 5% annual interest rate, calculate the amount of interest she must pay if the loan period is 1 year. a. P9 600.00 c. P6 000.00 b. P14 400.00 d. P12 000.00

Answers Key

Activity 1 Interest at 3% for 2 yrs = 6, 000 Interest at 3% for 3 yrs = 9, 000

Activity 2

Evaluation 1. 2. 3. 4.

A B C D 5. C

Amount to pay at the end of 1 year = 42, 400 Amount to pay at the end of second year = 44, 944 Amount to pay at the end of third year = 47,, 640.64

Analysis 1. 2. 3. 4. 5.

SI SI CI CI SI

References General Mathematics Orlando Oronce pp 186- 200 General Mathematics for Senior High School –Core Subject A Comprehensive Approach Winston S. Sirug, Ph.D pp113 - 126...