Compounding Periods

Compounding refers to earning interest on both the money you originally invest and on the interest that money earns over time. 

➡️ Daily Compounding means interest is calculated and added every day instead of monthly or yearly. This makes your money grow faster.

The formula is:

$$\mathrm{FV}=P\times {(1+\frac{r}{n})}^{n\times t}$$

Where:

• FV = Future Value
• P = Principal (initial amount) 
• r = Annual interest rate 
• n = Number of compounding periods per year (daily = 365)
• t = Number of years 

➡️Continuous Compounding means interest on your investment is being added at every possible moment — infinitely often.

Of course, this doesn’t happen in real life down to the nanosecond — it's more of a mathematical concept. But it helps us understand the maximum potential growth an investment could have if it compounded without stopping.  Continuous compounding is like interest earning interest, at every instant. It’s the limit of compounding as the number of compounding periods per year goes to infinity.

The formula is:

$$A = P \times e^{rt}$$

Where:

• FV = Future value

• P = Principal (initial investment)

• r = Annual interest rate

• t = Time in years

• e = Mathematical constant

➡️Effective Annual Rate (EAR) sometimes called Effective Annual Yield (EAY) is the true interest rate paid or earned over a year. it shows the real return or cost on an investment or loan.

The formula is:

If you know the nominal annual interest rate (r) and the number of compounding periods per year (n), you can calculate EAR using:

$$\text{EAR}={(1+\frac{r}{n})}^n-1$$

Where:

• r = Nominal annual interest rate

• n = Number of compounding periods per year

Note: The Effective Annual Rate helps you understand the real value of money in financial decisions. Whether you're comparing loans, savings accounts, or investments — EAR gives you the full picture.