# Difference between simple and compound interest

## Definitions and meanings:

The fee that a lender charges for an amount of money lent to a borrower is known as interest. Interest is usually charged in percentage terms.

### Simple Interest:

If interest is charged only on the principal amount of loan given to the borrower, the interest in known as simple interest.

### Compound Interest:

If interest is charged on principal amount as well as the interest already charged on the principal amount such that this interest amount is added to the principal amount is known as compound interest. Thus as the word compound suggests, the interest is charged on two elements i.e., principle amount and any interest already earned thereon.

## Difference between simple and compound interest:

The main points of difference between simple interest and compound interest are given below:

### 1. Effective rate of interest:

For the same percentage/rate of interest, simple interest is always lower than the compound interest for the same principal amount. The reason being simple interest is only charged on the principal amount of loan, whereas compound interest is charged on the principal amount plus accumulative amount of interest already charged. This makes the effective interest rate of compound interest higher than simple interest.

### 2. Calculations and formulas:

The calculations of simple interest are easy to understand and straight forward. The calculations of compound interest can become difficult and complicated especially if the calculations include long-term loans.

Formula for simple interest:

I = p × r × n

Where;

• I = Simple interest
• p = Principal Amount
• r = Rate of interest
• n = number of years of loan

Formula for compound interest:

I = p × [1-(1 + r/t)n]

Where;

• I = Compound interest
• p = Principal Amount
• r = Rate of interest
• n = number of years of loan
• t= number of times of compounding

Example:

A borrower takes a loan of \$50,000 on simple interest rate at 6% per annum. If the duration of loan is three years, the effective charge to the borrower would be:

I = p × r × n
= \$50,000 × (6/100) × 3
= \$50,000 × 0.06 × 3
= \$50,000 × 0.18
=\$9,000

Total amount to be repaid = Principle + Interest
= \$50,000 + \$9,000
= \$59,000

If the loan is borrowed on the same terms but compound interest is applied, then the effective charge to the borrower or profit for the lender would be computed as below:

I = p × [1-(1 + r/t)n]
= \$50,000 × [1-(1 + (6/100))3]
= \$50,000 × [1- (1.06)3]
= \$50,000 × (1-1.191016)
= \$50,000 × 0.191016
= \$9,550.8

Total amount to be repaid = Principle + Interest
= \$50,000 + \$9,550.8
= \$59,550.8

So, in above example, if simple interest is applied the borrower will have to repay a sum of \$59,000, while if compound interest is applied the borrower will pay a sum of \$59,550.8.

### 3. Application:

The simple interest is usually applied in car loans and leases. Borrowers also use and prefer to borrow loans on simple interest rates because in this way they can avoid the risk of overpaying their interest and also a predetermined liability creates certainty. Simple interest is also applied to normal investments including risk free investment accounts and certificate deposits. The compound interest is used mostly for the purposes of savings especially by pension funds, insurance companies etc. This type of interest provides benefit to the depositor or lender. Compound interest is applied by the banks upon the fixed savings deposits of lenders where the lender cannot withdraw their deposits for a certain span of time during which their investment is compounded based on the borrowing rate of bank. Credit card companies apply compound interest rate and charge the card holder on principal plus the accumulated interest amount.

 Simple interest vs Compound interest
Effective interest Rate
The effective interest rate of compound interest is higher The effective interest rate of simple interest is lower
Calculations and formulas
Compound interest calculations can become complicated P× [1-(1 + R/t)n] Simple interest is easy to calculate P × R× n
Application
Compound interest is used mostly by lenders for growth in their investments Simple interest is usually preferred by borrowers to increase certainty and decrease their borrowing cost

## Conclusion:

In practice, simple interest is applied where a business needs to minimize its risk of borrowing. Simple interest rate is in nature favorable for the borrower because of a fixed cash outflow. Compound interest is suitable for savings because it has a multiplier effect therefore investments in compound interest rate are normally for longer periods. However, in essence whichever type of interest is applied it will end up increasing the wealth of the lender.