The Difference between Simple Interest and Compound Interest Formulas
What is Simple Interest?
Simple interest is an easy calculation of interest that is based only on the principal amount. Simply put, simple interest is calculated based only on the amount borrowed or invested, without factoring in adding any interest earned to the principal.
The formula for simple interest is:
I = P x R x T
Where:
I = Interest
P = Principal amount
R = Rate of interest
T = Time
For example, if you borrowed $1000 at a 5% interest rate for one year, your simple interest would be:
I = 1000 x 0.05 x 1
I = $50
What is Compound Interest?
Compound interest is the interest calculation that factors the interest earned on the principal amount plus accumulated interest. In simple terms, compound interest means earning interest on the interest earned.
The formula for compound interest is:
A = P(1+r/n)^(nt)
Where:
A = Final amount
P = Principal amount
r = Interest rate
n = Number of times interest is compounded per year
t = Time in years
For example, if you invested $1000 in a savings account at a 5% interest rate compounded annually for one year, your compound interest would be:
A = 1000(1+0.05/1)^(1×1)
A = $1,050
The main difference between simple interest and compound interest is that simple interest only calculates interest on the principal amount, while compound interest calculates interest on the principal amount plus accumulated interest. As a result, compound interest usually yields higher returns over time compared to simple interest.
In conclusion, both simple interest and compound interest are essential calculations in finance. Still, compound interest is the preferable calculation for investments since it’s more accurate and yields higher returns over time.
Table difference between simple interest and compound interest formula
| Formula | Simple Interest | Compound Interest |
|---|---|---|
| Principal Amount | P | P |
| Rate of Interest | R | R |
| Time | T | T |
| Formula | SI = (P x R x T) / 100 | CI = P [(1 + R/n)^(nt) – 1] |
| Frequency of Compounding | NA | ‘n’ times in a year |
| Calculation of Interest | Interest is calculated only on the principal amount. | Interest is calculated on both the principal amount and the interest earned in previous periods. |
| Amount at Maturity | A = P + SI | A = P [(1 + R/n)^(nt)] |