Simple Interest and Compound Interest

Interest is earned when money is given to someone else to use, for example if it is deposited with a bank orloaned to an individual. There are two common ways of calculating interest.

Simple Interest is interest earned on the principal only. In other words, interest income will be distributed to investors and no further interest will be earned from interest income. The equation for finding simple interest is:

A = P + (P x r x t)

where

A = Total amount due to the investor

P = Principal

r = Annual interest rate (decimal)

t = Number of years (time)

Bozo put As. 1,000 in the bank for 6 months at a 10% interest rate. Find how much money will he have in his account at the end of six months.

A = P + (P x r x t)

A = 1,000 + (1,000 x 0.1 x 0.5)

A = 1,000 + (100 x 0.5)

A = 1 ,000 + 50

A = As. 1 ,050

The amount of money Bozo will have in his account at the end of six months is Rs. 1,050

In simple interest, you earn interest payments from the principal only. In Compound Interest, you reinvest the interest payments and earn interest on the interest amount as well.

Let us say you are investing Rs. 1,000 at 10% compound interest. After a specified period of time, called compounding period (let us assume this is 1 year for this problem), you calculate the simple interest on the principal, i.e. 10% of Rs. 1000 = Rs. 100 and add it to the principal giving you Rs. 1,000 + Rs. 100 = Rs. 1,100. This new amount will be the principal for the next time period of1 year and so on. Thus for the second year, the interest will be 10% of Rs. 1100 = Rs. 110.

The period of compounding is important because as the period of compounding becomes lesser, the interest amount joining the capital becomes higher.

* If an amount is invested under compound interest for a time period that is less than the compounding period, then it is equivalent to investing the money under simple interest at the same interest rate.

* An amount invested under compound interest will always earn more interest than the same amount invested under simple interest at the same interest rate, provided the time it is invested for is more than the compounding period.

*  Intuitively, we can see that a lower compounding period means a, higher totaI amount due to the investor since we are adding the interest to the principal more often.

The equation for finding compound interest is:

A = P (1 + r/k)kxn

Where

A = Amount due to the investor

P = Principal

r = Annual rate (in decimal or per unit)

k = number of times compounding per year

n = number or years

John deposited Rs. 1,000 at a 10% interest rate for 5 years. How much more money will John have in his account from compound interest than from simple interest if it is compounded semi-annually?

Simple Interest:

A = P + (P x r x t)

A = 1,000 + (1,000 x 0.1 x 5)

A = 1,000 + (100 x 5)

A = 1,000 + 500

A = Rs. 1,500

Compound Interest:

A = ( 1 + r/k )kxn

A = ( 1 + 0.1/2 )2*5

A = 1,000 (1 + 0.05)10

A = 1,000 x 1.62889

A = Rs. 1,628.89

Rs. 1,628.89 (compound interest) – Rs.1,500 (simple interest) = Rs. 128,89. Thus, John will make Rs. 128.89 more from compound interest than from simple interest.

THE RULE OF 72

The rule of 72 is a quick way to show how long it will take to double your money under

Compound interest.

The equation for the rule of 72 is:

Number of years for money to double = 72 / Anual Interest rate

At 8% interest, it will take 72/8 = 9 years for your money to double.

Here are more examples:

At 6%, it will take 12 years ( 72/6 = 12 )

At 12%, it will take 6 years ( 72/12 = 6 )

The rule of 72 is a short cut to estimate the magic of compound interest that makes your money grow.

Remember that the rule of 72 is an approximation and its accuracy reduces as the interest rate becomes high.

CONCEPTS

Compound Interest Under Complex Conditions

For a principal amount P, we have: