basic math assigment

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COLLEGE:IPGM KAMPUS TENGKU AMPUAN AFZAN

KUALA LIPIS PAHANG

NO. NAME I/C NO.

1 MOHAMAD NAZIF BIN ISHAK 92

2 MUHAMAD ASHRAF BIN MUSTAPHA 920203035687

NAME:MOHAMAD NAZIF BIN ISHAK

92

MUHAMAD ASHRAF BIN MUSTAPHA

920203-03-5687

UNIT:PPISMP PAI(SJKC) SEM 1

SHORT COURSEWORK

SUBJET:BASIC MATHEMATICS

COURSE:PREPARATION COURSE BACHELOR OF EDUCATION

PROGRAM(SEMESTER 1)

LECTURER NAME:MADAM HJH. HALIMAH BINTI HJ. HALIMI

TARIKH HANTAR:26.8.2010



INDEX



INTRODUCTION



INTEREST

Interest is a fee paid on borrowed assets. It is the price paid for the use of

borrowed money, or, money earned by deposited funds. Assest that aresometimes lent with interest include money, shares, consumer goodsthrough hire purchase, major assets such as aircraft, and even entirefactories in finance lease arrangements. The interest is calculated uponthe value of the assets in the same manner as upon money. Interest canbe thought of as "rent of money". For example, if you want to borrowmoney from the bank, there is a certain rate you have to pay according tohow much you want loaned to you.

Interest is compensation to the lender for forgoing other usefulinvestments that could have been made with the loaned asset. Theseforgone investments are known as the opportunity cost. Instead of thelender using the assets directly, they are advanced to the borrower. Theborrower then enjoys the benefit of using the assets ahead of the effortrequired to obtain them, while the lender enjoys the benefit of the feepaid by the borrower for the privilege. The amount lent, or the value of the assets lent, is called the principal. This principal value is held by theborrower on credit. Interest is therefore the price of credit, not the price of money as it is commonly believed to be.The percentage of the principalthat is paid as a fee (the interest), over a certain period of time, is calledthe interest rate.



SIMPLE INTEREST

Simple interest is calculated only on the principal amount, or on thatportion of the principal amount which remains unpaid.

The amount of simple interest is calculated according to the followingformula:

where r is the period interest rate (I/m), B0 the initial balance and m the

number of time periods elapsed. To calculate the period interest rate r , one divides the interest rate I bythe number of periods m.

For example, imagine that a credit card holder has an outstandingbalance of $2500 and that the simple interest rate is 12.99% per annum. The interest added at the end of 3 months would be,

and he would have to pay $2581.19 to pay off the balance at this point.If instead he makes interest-only payments for each of those 3 months atthe period rate r , the amount of interest paid would be,

His balance at the end of 3 months would still be $2500.

In this case, the time value of money is not factored in. The steadypayments have an additional cost that needs to be considered whencomparing loans. For example, given a $100 principal:

• Credit card debt where $1/day is charged: 1/100 = 1%/day =7%/week = 365%/year.

• Corporate bond where the first $3 are due after six months, and thesecond $3 are due at the year's end: (3+3)/100 = 6%/year.

• Certificate of deposit (GIC) where $6 is paid at the year's end: 6/100= 6%/year.

There are two complications involved when comparing different simpleinterest bearing offers.



1. When rates are the same but the periods are different a directcomparison is inaccurate because of the time value of money.Paying $3 every six months costs more than $6 paid at year end so,the 6% bond cannot be 'equated' to the 6% GIC.

2. When interest is due, but not paid, does it remain 'interest payable',like the bond's $3 payment after six months or, will it be added tothe balance due? In the latter case it is no longer simple interest,but compound interest.

A bank account offering only simple interest and from which money canfreely be withdrawn is unlikely, since withdrawing money and immediatelydepositing it again would be advantageous.

Simple interest is the most basic type of interest. In order to understandhow various types of transactions work, it helps to have a completeunderstanding of simple interest.

For example, you may pay interest on a loan, and it is important tounderstand how interest works. Better yet, your bank may be paying youinterest on your deposits – and you can maximize your earnings byknowing more about interest.

Simple Interest Formula

If you want to calculate simple interest, use this formula:

I=P r t

In other words Interest (I) is calculated by multiplying Principal (p) times

the Rate (r) times the number of Time (t) periods.

For example, if I invest $100 (the Principal) at a 5% annual rate for 1 yearthe simple interest calculation is:

I=P r t

$5 = $100 x 5 % x 1 yr



Simple Interest Limitations

Simple interest is a very basic way of looking at interest. In fact, yourinterest – whether you’re paying it or earning it – is usually calculatedusing different methods. However, simple interest is a good start thatgives us a general idea of what a loan will cost or what an investment willgive us.

The main limitation that you should keep in mind is that simple interestdoes not take compounding into account.

Calculate Simple Interest

1. Principal X Rate X Time = Interest Amount

Principal is the amount upon which interest is being earned, rate is theinterest rate in percent or decimal form and time is the time uponwhich interest is being earned. Example:

$100,000(Principal) X 0.08(8% Rate) X 1 Year (Time) = $8000 Interest

2. Principal X {1 + (Rate X Time)} = Total Amount

All we're doing here is getting the total amount in hand at the end of the interest bearing period. In this first calculation, it's for one year, atthe end of which, we'll have the original $100,000 + Interest.

$100,000 X {1 + (.08 X 1)} = $100,000 X 1.08 = $108,000

3. Let's do that again for three years:

Here we'll multiply the .08 (8%) rate times 3 years to equal .24.

$100,000 X {1 + .24} = $124,000



TYPE OF INTEREST

THERE ARE TWO TYPE OF INTEREST:

➢ SIMPLE INTEREST➢ COMPOUND INTEREST

SIMPLE INTEREST

When you deposit money in a saving account,your deposit is called

PRINCIPAL. The bank takes money and invest it. In return,the bank pays

you interest based on the interest rate. Simple interest is interest paid

only the PRINCIPLE.

Simple interest can be calculate using this formula:

I=PRT

I=INTEREST

P=PRINCIPLE

R=THE INTEREST RATE PER YEAR

T=THE TIME IN YEAR



EXAMPLE 1:-

You borrow RM10,000 for 3 years at 5% simple annual interest. What is

the interest for 3 years?

INTEREST=PxRxT

=10,000 x 0.05 x 3

= 1,500

EXAMPLE 2:-

You boroow RM10,000 for 60 days at 5% simple interest per year(assume

a 365 day year). What is your interest for 60 days?

INTEREST=PxRxT

= 10,000 x 0.05 x (60/365)

= 82.1917

We also can use this formula to calculate:-



THE SIMPLE INTEREST FORMULA:-

FV=PV(1+rt)

Where

FV= Future Value (RM)

PV= Present Value (RM)

r= Interest rate

t=Time (Years)



COMPOUND INTEREST

Compound interest is very similar to simple interest; however, with time,the difference becomes considerably larger. This difference is becauseunpaid interest is added to the balance due. Put another way, theborrower is charged interest on previous interest. Assuming that no partof the principal or subsequent interest has been paid, the debt iscalculated by the following formulas:

where Icomp is the compound interest, B0 the initial balance, Bn the balanceafter n periods (where n is not necessarily an integer) and r the periodrate.

For example, if the credit card holder above chose not to make anypayments, the interest would accumulate



So, at the end of 3 months the credit card holder's balance would be$2582.07 and he would now have to pay $82.07 to get it down to theinitial balance. Simple interest is approximately the same as compoundinterest over short periods of time, so frequent payments are the best(least expensive) payment strategy.

A problem with compound interest is that the resulting obligation can bedifficult to interpret. To simplify this problem, a common convention ineconomics is to disclose the interest rate as though the term were oneyear, with annual compounding, yielding the effective interest rate.However, interest rates in lending are often quoted as nominal interestrates (i.e., compounding interest uncorrected for the frequency of compounding).

Loans often include various non-interest charges and fees. One exampleare points on a mortgage loan in the United States. When such fees arepresent, lenders are regularly required to provide information on the 'true'cost of finance, often expressed as an annual percentage rate (APR). TheAPR attempts to express the total cost of a loan as an interest rate after including the additional fees and expenses, although details may vary by jurisdiction.

In economics, continuous compounding is often used due to its particularmathematical properties.

Compound Interest Use this online calculator if you are borrowing money or you are lendingmoney. This calculator enables you to determine how much interest willbe paid or accumulated.See also: Free Amortization Schedule calculator

Top of Form



Bottom of Form

Step 1: Enter thePrincipal (the amount of money borrowed or to be lent).

Step 2: Enter theRate (The annual percentage of interest)

Step 3: Enter thelength of time in years the money will be borrowed or lent for.

Example:

Denise wants to borrow $5000.00 to purchase a used car. She wants to beable find out how much the car will cost her if she borrows the $5000.00at an interest rate of 8% for 4 years. Thus, she will enter $5000.00 in thecolumn for Principal. She will enter 8 in the column for rate and 4 in thecolumn for years. She will then click calculate. The amount she is actuallypaying for her $5000.00 is $6802.44. The total amount of interest she willbe charged for borrowing the $5000.00 is $1802.44.

Compound Interest

When you borrow money from a bank, you pay interest. Interest is really afee charged for borrowing the money, it is a percentage charged on theprinciple amount for a period of a year - usually.

If you want to know how much interest you will earn on your investmentor if you want to know how much you will pay above the cost of theprincipal amount on a loan or mortgage, you will need to understand howcompound interest works.

* Compound interest is paid on the original principal and on theaccumulated past interest.

Formula:

P is the principal (the initial amount you borrow or deposit)

COMPOUND INTEREST

Principal Months1 = .082 = .173 = .254 = .335 = .426 = .50

7 = .588 = .679 = .7510 = .8311 = .92

Rate

Years

Amount

Interest

Clear



r is the annual rate of interest (percentage)

n is the number of years the amount is deposited or borrowed for.

A is the amount of money accumulated after n years, including interest.

When the interest is compounded once a year:

A = P(1 + r)n

However, if you borrow for 5 years the formula will look like:

A = P(1 + r)5

This formula applies to both money invested and money borrowed.

Frequent Compounding of Interest:

What if interest is paid more frequently?Here are a few examples of the formula:

Annually = P × (1 + r) = (annual compounding)

Quarterly = P (1 + r/4)4 = (quarterly compounding)

Monthly = P (1 + r/12)12 = (monthly compounding)



PART C:

REFLECTION

First of all, I would like to thank Allah S.W.T for blessing and helping me to

complete this tasks. Secondly, I want to thank my family because always

give support to complete this task.. Next, I would like to thank my lecturer

for his help and patience. Lastly, to my friends in this institut and other

friends from another institut for their support and all of the advices that

given by them through many sources.

This task has helped me to know myself better. It has taught me

skills that I will take with me to my future courses. I will know how to

collect research in many ways. By doing this tasks, I have learnt about

Fibonacci sequence and how the numbers were created and be related

with nature creations found in earth such as the rabbits, tree and

pineapple. The assignment given also help me to learn and understand

more about two types of interest which are simple interest and compound

interest.I learnt how to use the formula to calculate compound interest,

total instalment price, finance charge and so on. This knowledge will help

me in the future.

Sometimes,i realised that we cant do works alone.To complete this

assignment i also cooperate with my friends.Everone of us will help each

other out if a co-worker has a problem. Also, working in teams is

important in many jobs. The team project helped me to learn how to be a

part of a team. For example, while we were solving the problems in

Attachment 1, all of my group members give their ideas and views. I



found that it is important to work in group to solve problems. This is where

my critical thinking skills came in handy.

Learning new information is something that most people do each

day, but may not even notice. So I decide to follow these principals, be

good and kind to yourself and others, care for yourself, your work and for

others and always try to make a positive difference. It is as simple as that.

It is always based on those guidelines that I try to function as well as I

can.

In closing, I would like to add that I have really enjoyed the

experience of completing this task. Thank you.

PART D:



Part B

PART B (Budget Proposal And Loan Schemes).

Task 1:

INFORMATION ABOUT THE PERSONAL LOAN SCHEMES

– Bank Simpanan National.

– CIMB Bank .

– Bank Rakyat .

BANK SIMPANAN NATIONAL

Year 1-2 3-5

Interest Rate 3.5% 4.49%

Loan Amount

RM5000 Rm432 Rm223 Rm158 Rm102



Interest rate of 4.49% for 5 years loan amount needed : Rm5000

4.49100 x 5000 = Rm 224.50

Rm 224.50 x 5 = Rm 1122.50

112.50+500060 = Rm 102.00

CIMB ISLAMIC BANK

Year 1 2 3 4 5

Month 12 24 36 48 60

Interestrate

0.46%

Loan

Amount

Rm 5000 Rm444 Rm 234 Rm 164 Rm129 Rm 108

Interest rate 0.46% Permonth

Loan needed : Rm 5000

0.46100 x 5000 = Rm 23.00

Rm 23.00 x 60 = Rm 1380

1380+500060 = Rm 108.00

BANK RAKYAT

Year 1 2 3 4 5

Month 12 24 36 48 60

Interest

rate

4.9% 5.1% 5.1% 5.5% 5.5%

Loan

Amount

Rm 5000 Rm438 Rm 230 Rm 161 Rm128 Rm 107

Interest rate of 5.5% of 5years.



Loan needed : Rm 5000

5.5100 x 5000 = Rm 275.00

Rm 275.00 x 5 =Rm 1375

1375+500060 = Rm 106.25

= Rm 107.

Comparing And Contarasting Between Personal Loan Schems

Name Of Bank

Catagories

Bank BSN CIMB Islamic Bank Bank Rakyat

Financing Amount Rm 5000

(5 times monthly

incomes)

Rm 5000

(5 times monthly

income)

Rm 5000

(up to 5 times

monthly income)

Profit Rate 4.79% a year till

5 years

5.10% a year till

10 years.

0.46% month 5.5% a year till 5

years

5.70% a year till

10 years

Averange Of Age 21 – 58 years old 18 – 58 years old 18 – 58 years old

Payment Capasity

Subject to total

deducations not

exceeding 60%

(goverment) or

50% (private).

By ‘biro angkasa ’

which deducation

income is not

more than 60%

from the monthly

income.

Monthly

deducation

exceeding 60% of

gross monthly

income.

Task 2 :

Planning On the Personal Budget .

Personal Budget Amount

Food And Drinks Rm 100

Education Rm 45



Saving Rm 100

Others Rm 75

Total Amount = Rm 320

Personal Budget For a Month

Formula : Annual Budget = Monthly Budget x 12

320 x 12 = Rm 3840

Food And Drinks = Rm 100320 x 100 = 31.25%

Education = Rm 45320 x 100 = 14.06%

Saving = Rm 100320 x 100 = 31.25%

Others = Rm 75320 x 100 = 23.44%

Annua l Expenses

Base on the monthly expenses , we spent the allowence money Rm 430

for food and drinks that Rm 100 . The percentage of food and drinks from

the pie chart is 31.25% , besides that , we also spent our money forsaving Rm 100 so , the percentage is also 31.25% . As a trainer teacher ,

we need to buy many refrence book and learns sources . So that we

must spent money for our education payment at least Rm 45 , so the

percentage is 14.06% . Lastly the others 23.44% is our personal budget

such as our brodband bil , ticket us or train payment , clothes and etc we

spant about RM 75.



Decision Choosing A Personal Loan

Loan:

From our searching , we had made our last decision to choose “Bank

Rakyat ” as the best to do personal loan .

Decision :

There are many benifits of being the loaner in “ Bank Rakyat ” .

First , it is suitable for our purpose buying a laptop and printer

for our personal using that is not false in islam but for our

convenience and security . The interest of “ Bank rakyat ” of 5.5%

for 5 years . The payment For 1 month just Rm107.00 . Moreover

with the money in hand that we can pay the loan with our

allowance . Beside , the requirement and qualitification is not very

hard to us use this loan .

basic math assigment

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