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What is Compound Interest?

Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods. Unlike simple interest, which only earns interest on the original amount, compound interest allows your money to grow exponentially over time.

Albert Einstein reportedly called compound interest "the eighth wonder of the world," saying: "He who understands it, earns it; he who doesn't, pays it."

The Compound Interest Formula

The basic formula for compound interest is:

$$A = P \left(1 + \frac{r}{n}\right)^{nt}$$A=P(1+nr​)nt

Where:

• A = Final amount (principal + interest)
• P = Principal (initial investment)
• r = Annual interest rate (as a decimal)
• n = Number of times interest compounds per year
• t = Time in years

For continuous compounding, the formula becomes:

$$A = Pe^{rt}$$A=Pert

The Rule of 72

A quick mental math trick to estimate how long it takes to double your money:

$$\text{Years to double} = \frac{72}{\text{Interest Rate}}$$Years to double=Interest Rate72​

For example:

• At 6% interest: 72 ÷ 6 = 12 years to double
• At 8% interest: 72 ÷ 8 = 9 years to double
• At 12% interest: 72 ÷ 12 = 6 years to double

Why Compound Frequency Matters

The more frequently interest compounds, the more you earn. Think of it as: how often the bank calculates and adds interest to your balance.

• Annual compounding: Interest added once per year
• Monthly compounding: Interest added 12 times per year
• Daily compounding: Interest added 365 times per year
• Continuous compounding: Interest added infinitely (theoretical maximum)

At a 10% annual rate on $10,000 over 10 years:

• Annual compounding: $25,937
• Monthly compounding: $27,070
• Daily compounding: $27,179
• Continuous compounding: $27,183

Real vs Nominal Returns: Understanding Inflation

When planning long-term investments, it's crucial to understand the difference between nominal returns (the number you see) and real returns (actual purchasing power).

Nominal Return: The raw percentage your investment grows – what your account statement shows.

Real Return: Your return after accounting for inflation – what your money can actually buy.

$$\text{Real Value} = \frac{\text{Nominal Value}}{(1 + \text{Inflation Rate})^{\text{Years}}}$$Real Value=(1+Inflation Rate)YearsNominal Value​

A simpler approximation:

$$\text{Real Return} \approx \text{Nominal Return} - \text{Inflation Rate}$$Real Return≈Nominal Return−Inflation Rate

Example: You invest $10,000 at 10% annual return for 20 years.

• Nominal value: $67,275 (what your account shows)
• With 3% inflation: $37,278 in today's purchasing power
• Inflation loss: $29,997 – nearly half your "gains"!

Historical inflation rates vary by country, but a common assumption for developed economies is 2-3% annually. During high-inflation periods, this can exceed 5-10%.

Tips for Maximizing Compound Interest

1. Start early – Time is your greatest ally. Even small amounts grow significantly over decades.
2. Be consistent – Regular contributions amplify the effect of compounding.
3. Reinvest returns – Don't withdraw interest; let it compound.
4. Seek higher rates – Even a 1% difference compounds to significant amounts over time.
5. Minimize fees – High fees erode your compounding gains.
6. Beat inflation – Ensure your real return is positive; otherwise, you're losing purchasing power.