Corporate practice bd
What-is-compound & simple-interest-rate? Key-differences
Compound interest is a method of calculating interest where interest is added to the principal amount, and then interest is earned on both the principal and the previously accumulated interest. In other words, interest is calculated on the initial principal and also on the accumulated interest from previous periods. This leads to exponential growth of the invested or loaned amount over time.
Key differences between simple and compound interest rates:
Calculation Method:
Simple Interest: With simple interest, interest is calculated only on the initial principal amount. The interest remains constant throughout the investment or loan term.
Compound Interest:
Compound interest takes into account the accumulated interest in addition to the initial principal amount. Interest is earned not only on the principal but also on the interest accrued from previous periods.
Effect on Total Amount:
Simple Interest: With simple interest, the total amount grows linearly over time. The interest earned or paid remains constant for each period.
Compound Interest:
Compound interest leads to exponential growth or compounding of the total amount over time. As interest is earned on both the principal and the accumulated interest, the total amount grows at an increasing rate.
Frequency of Calculation:
Simple Interest:
Interest is calculated only once, typically at the end of the investment or loan term.
Compound Interest:
Compound interest can be calculated at different intervals, such as annually, semi-annually, quarterly, monthly, or even daily. The more frequently interest is compounded, the faster the total amount grows.
Formula:
Simple Interest:
The formula for calculating simple interest is: Simple Interest=P×r×t\text{Simple Interest} = P \times r \times tSimple Interest=P×r×t, where PPP is the principal amount, rrr is the interest rate per period, and ttt is the time period.
Compound Interest:
The formula for calculating compound interest is: A=P×(1+rn)ntA = P \times \left(1 + \frac{r}{n}\right)^{nt}A=P×(1+nr)nt, where AAA is the total amount, PPP is the principal amount, rrr is the annual interest rate, nnn is the number of times interest is compounded per year, and ttt is the time in years.
In summary, compound interest takes into account the effect of earning interest on previously accumulated interest, leading to exponential growth of the total amount over time, while simple interest calculates interest based only on the initial principal amount.