When you borrow money from someone, whether it is an individual or a financial institution, you need to pay a specific amount of extra money against that borrowing. This extra money on the actual amount is known as interest. Usually, a fixed percentage is set for this payment. Let’s discuss below the different types of interest.
Different Types of Interest
- Simple Interest
- Discrete Compound Interest
- Continuous Compound Interest
Now it’s time to discuss them one by one in detail to understand their actual meaning and use.
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Simple Interest (or Straight Line)
Simple interest is calculated only on the principal amount. The principal and interest are kept separate while calculating simple interest.
In other words, while calculating interest for the next period, the interest incurred in one year is not added to the principal. The following formula is used to calculate simple interest:
FV = PV + (PV × i × n)
Example:
Assume that an individual has 100 dollars today and wants to invest this amount in a bank for five years. The bank offers an interest rate of 7%.
By using the above formula, the simple interest on the investment can be calculated.
FV = PV + (PV × i × n)
For the term of investment:
- FV is the future value (simple interest accrued).
- PV is the amount invested = 100 dollars.
- i is the interest rate = 7% = 0.07.
- n is the time period = 5 years.
Putting the values into the formula:
FV = 100 + (100 × 0.07 × 5)
FV = 100 + (7 × 5)
FV = 100 + 35
FV = 135 dollars
The future value of the investment after five years is 135 dollars. Out of this, 35 dollars is the interest earned on the initial investment of 100 dollars.
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Discrete Compound Interest
Discrete compound interest is one of the most commonly used tools in financial management, especially in discounting and NPV calculations.
Compound interest considers both the principal and the interest already earned. Unlike simple interest, the interest earned in one period is added to the principal for calculating the next period’s interest.
In other words, interest is calculated on principal + accumulated interest, and this compounding happens at specific intervals.
Compounding can be:
- Monthly
- Quarterly
- Semi-annually
- Yearly
Annual (Yearly) Compounding Formula:
FV = PV × (1 + i)ⁿ
Monthly Compounding Formula:
FV = PV × (1 + (i / m))^(m × n)
Where:
- m = number of compounding periods per year
Example:
Using the same data as the previous example:
FV = PV × (1 + i)ⁿ
FV = 100 × (1 + 0.07)⁵
FV = 100 × (1.07)⁵
FV = 100 × 1.40255
FV = 140.255
Here, the future value is higher than in simple interest.
Monthly Compounding:
FV = 100 × (1 + (0.07 / 12))^(12 × 5)
FV = 100 × (1 + 0.005833)⁶⁰
FV = 100 × (1.005833)⁶⁰
FV = 100 × 1.4176
FV = 141.76
The investor’s wealth increases more with more frequent compounding.
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Continuous (or Exponential) Compound Interest
Continuous compounding is another type of compound interest where compounding happens infinitely many times per year.
Formula:
FV = PV × e^(i × n)
Where:
- e = constant (≈ 2.718)
Example:
Using the same investment:
FV = 100 × e^(0.07 × 5)
FV = 100 × e^0.35
FV = 100 × 1.419
FV = 141.9
When the investor chooses continuous compounding, the final wealth is the highest compared to other methods.
