Arithmetic - Interest

What is 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. Assets that are sometimes lent with interest include money, shares, consumer goods through hire purchase, major assets such as aircraft, and even entire factories in finance lease arrangements. The interest is calculated upon the value of the assets in the same manner as upon money. Interest can be thought of as "rent of money". For example, if you want to borrow money from the bank, there is a certain rate you have to pay according to how much you want loaned to you.
Interest is compensation to the lender for foregoing other useful investments that could have been made with the loaned asset. These foregone investments are known as the opportunity cost. Instead of the lender using the assets directly, they are advanced to the borrower. The borrower then enjoys the benefit of using the assets ahead of the effort required to obtain them, while the lender enjoys the benefit of the fee paid 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 the borrower 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 principal that is paid as a fee (the interest), over a certain period of time, is called the interest rate.

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

The formula is as follows:

I = Prt

I = interest
P = principal
r = interest rate (per year)
t = time (in years or fraction of a year)

A real-life example:
My Dad deposited $400 earning simple interest of 4% per year. Calculate the simple interest at the end of one year and at the end of five months.

Solution: I = $400 x 0.04 x 1= $16.00 (substitute the known values)


What is Compound Interest?
When you borrow money from a bank, you pay interest. Interest is really a fee charged for borrowing the money, it is a percentage charged on the principle amount for a period of a year - usually.If you want to know how much interest you will earn on your investment or if you want to know how much you will pay above the cost of the principal amount on a loan or mortgage, you will need to understand how compound interest works.

The formula:

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

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

Annually = P × (1 + r) = (annual compounding)
Quarterly = P (1 + r/4)4 = (quarterly compounding)
Monthly = P (1 + r/12)12 = (monthly compounding)

An example for compound interest:

My Dad takes a loan of $30,000 from DBS for 2 months to start a business with his 2 other friends.The interest per year is 2%.He would pay once every month.So the total amount is $30,000 X 2/100 X 2/12 =$100 (2 months).By the nd of the 2 months, he needs to pay the principle+the interest=$(30000+100)=$30100.