COMPOUND INTEREST is the EIGHTH WONDER of the world.He who UNDERSTANDS IT earns it..He who doesn’t PAYS IT..

### SIMPLE INTEREST AND COMPOUND INTEREST

#### INTEREST:

Interest may be defined as the charge for using the borrowed money. It is an expense for the person who borrows money and income for the person who lends money. Interest is charged on *principal amount* at a certain rate for a certain period. For example, 10% per year, 4% per quarter or 2% per month etc. Principal amount means the amount of money that is originally borrowed from an individual or a financial institution. It does not include interest. In practice, the interest is charged using one of two methods. These are:

- Simple interest method
- Compound interest method

**SIMPLE INTEREST METHOD:**

Under this method, the interest is charged only on the amount originally lent (principal amount) to the borrower. Interest is not charged on any accumulated interest under this method. Simple interest is usually charged on short-term borrowings.

**SIMPLE INTEREST FORMULA:**

Simple interest can be easily computed using the following formula:

*Where;*

I = Simple interest in dollars

P = Principal amount

i = rate of interest

n = number of periods

### Example 1:

A loan of $10,000 has been issued for 6-years. Compute the amount to be repaid to the lender if simple interest is charged @ 5% per year.

#### Solution:

P = $1,000; i = 5%; n = 5

By putting the values of P, i and n into the simple interest formula:

= $10,000 × 5% × 6

= $10,000 × .05 × 6

= $3,000

At the end of sixth year, the amount of $13,000 ($10,000 principal + $3,000 accumulated interest) will be repaid to the lender

#### Compound interest method:

Compounding of interest is very common. Under this method, the interest is charged on principal plus accumulated interest. The amount of interest for a period is added to the amount of principal to compute the interest for next period. In other words, the interest is reinvested to earn more interest. The interest may be compounded monthly, quarterly, semiannually or annually. Consider the following example to understand the whole procedure of compounding.

**COMPOUND INTEREST FORMULA:**

The above procedure of computing compound amount is lengthy and time consuming. Fortunately, a formula is available to compute compound amount for any number of periods. It is given below:

*Where;*

S = compound amount

P = Principal amount

i = rate of interest

n = number of periods

#### Compound interest is greater than simple interest:

Compound interest is greater than simple interest. The reason is very simple. Under simple interest system, the interest is computed only on principal amount whereas under compound interest system, the interest is computed on principle as well as on accumulated interest. Consider the following example for the explanation of this point

**EXAMPLE:**

A woman has deposited $6,000 in a saving account. Bank pays interest at a rate of 9% per year?

**Required: **Compute the amount of interest that will be earned over 12-year period:

- if the interest is simple?
- if the interest is compounded annually?

#### Solution:

**(1) Simple interest:**

= $6,000 × 0.09 × 12

= $6,480

**(2) Compound interest:**

= $6,000 × (1 + 9%)^{12}

= $6,000 × 2.813*

= $16,878

Interest: $16878 – $6,000 = $10,878

Notice that compound interest is more than simple interest by $4,398 ($10,878 – $6,480).

*Value of (1 + 9%)^{12} from future value of $1 table: 12 periods; 9% interest rate.

### DIFFERENCES BETWEEN SIMPLE INTEREST AND COMPOUND INTEREST:

BASIS FOR COMPARISON | SIMPLE INTEREST | COMPOUND INTEREST |
---|---|---|

Meaning | Simple Interest refers to an interest that is calculated as a percentage of the principal amount. | Compound Interest refers to an interest which is calculated as a percentage of principal and accrued interest. |

Return | Less | Comparatively high |

Principal | Constant | Goes on changing during the entire borrowing period. |

Growth | Remains uniform | Increases rapidly |

Interest charged on | Principal | Principal + Accumulated Interest |

Formula | Simple Interest = P*r*n | Compound Interest = P*(1 + r)^nk |

#### 1.How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per anum of simple interest?

#### 2.A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest. What is the rate of interest?

#### 3.What will be the ratio of simple interest earned by a certain amount at the same rate of interest for 6 years and that for 9 years?

#### 4.What should be the least number of years in which the simple interest on Rs.2600 at 6⅔% will be an exact number of rupees?

#### 5.A sum of money trebles itself in 15 years 6 months. In how many years would it double itself?

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