Simple interest is the type of interest that is calculated on the principal amount only, while compound interest is calculated on the principal amount plus any interest earned over time.
The formula for simple interest can be represented as follows:
I = P ⋅ r ⋅ t
where:
- I is the interest
- P is the principal amount
- r is the rate of interest
- t is the time period
For example, if you invest $1,000 at a simple annual interest rate of 5% for three years, the interest earned would be calculated as follows:
I = 1000 ⋅ 0.05 ⋅ 3 = 150
Therefore, the total amount to be paid after three years would be $1,150.
On the other hand, the formula for compound interest can be represented as follows:
$$A = P \cdot \left(1 + \frac{r}{n}\right)^{nt}$$
where:
- A is the total amount after n years
- P is the principal amount
- r is the annual interest rate
- n is the number of times interest is compounded per year
- t is the number of years
For example, if you invest $1,000 at a rate of 5% compounded annually for three years, the total amount earned would be calculated as follows:
$$A = 1000 \cdot \left(1 + \frac{0.05}{1}\right)^{1 \cdot 3} = 1157.63$$
Therefore, the total amount to be paid after three years would be $1,157.63.
As you can see from the above example, compound interest generates more returns than simple interest for the same principal amount, interest rate, and time period. That is why most loan and investment products use compound interest.