Financial Modeling Tutorials

- Excel Modeling
- Financial Functions in Excel
- Sensitivity Analysis in Excel
- Sensitivity Analysis
- Capital Budgeting Techniques
- Time Value of Money
- Future Value Formula
- Present Value Factor
- Perpetuity Formula
- Present Value vs Future Value
- Annuity vs Pension
- Present Value of an Annuity
- Doubling Time Formula
- Annuity Formula
- Present Value of an Annuity Formula
- Future Value of Annuity Due Formula
- Maturity Value
- Annuity vs Perpetuity
- Annuity vs Lump Sum
- Deferred Annuity Formula
- Internal Rate of Return (IRR)
- IRR Examples (Internal Rate of Return)
- NPV vs XNPV
- NPV vs IRR
- NPV Formula
- NPV Profile
- NPV Examples
- Advantages and Disadvantages of NPV
- Mutually Exclusive Projects
- PV vs NPV
- IRR vs ROI
- Break Even Point
- Break Even Analysis
- Breakeven Analysis Examples
- Break Even Chart
- Benefit Cost Ratio
- Payback Period & Discounted Payback Period
- Payback period Formula
- Discounted Payback Period Formula
- Payback Period Advantages and Disadvantages
- Profitability Index
- Feasibility Study Examples
- Cash Burn Rate
- Interest Formula
- Simple Interest
- Simple Interest vs Compound Interest
- Simple Interest Formula
- CAGR Formula (Compounded Annual Growth Rate)
- Growth Rate Formula
- Effective Interest Rate
- Loan Amortization Schedule
- Mortgage Formula
- Loan Principal Amount
- Interest Rate Formula
- Rate of Return Formula
- Effective Annual Rate
- Effective Annual Rate Formula (EAR)
- Compounding
- Compounding Formula
- Compound Interest
- Compound Interest Examples
- Daily Compound Interest
- Monthly Compound Interest Formula
- Discount Rate vs Interest Rate
- Discounting Formula
- Rule of 72
- Geometric Mean Return
- Geometric Mean vs Arithmetic Mean
- Real Rate of Return Formula
- Continuous compounding Formula
- Weighted average Formula
- Average Formula
- EWMA (Exponentially Weighted Moving Average)
- Average Rate of Return Formula
- Mean Formula
- Mean Examples
- Population Mean Formula
- Weighted Mean Formula
- Harmonic Mean Formula
- Median Formula in Statistics
- Range Formula
- Outlier Formula
- Decile Formula
- Midrange Formula
- Quartile Deviation
- Expected Value Formula
- Exponential Growth Formula
- Margin of Error Formula
- Decrease Percentage Formula
- Relative Change
- Percent Error Formula
- Holding Period Return Formula
- Cost Benefit Analysis
- Cost Benefit Analysis Examples
- Cost Volume Profit Analysis
- Opportunity Cost Formula
- Opportunity Cost Examples
- APR vs APY
- Mortgage APR vs Interest Rate
- Normal Distribution Formula
- Standard Normal Distribution Formula
- Normalization Formula
- Bell Curve
- T Distribution Formula
- Regression Formula
- Regression Analysis Formula
- Multiple Regression Formula
- Correlation Coefficient Formula
- Correlation Formula
- Correlation Examples
- Coefficient of Determination
- Population Variance Formula
- Covariance Formula
- Coefficient of Variation Formula
- Sample Standard Deviation Formula
- Relative Standard Deviation Formula
- Standard Deviation Formula
- Standard Deviation Examples
- Effect Size
- Sample Size Formula
- Volatility Formula
- Binomial Distribution Formula
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- Central Limit Theorem
- Poisson Distribution
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- Hypothesis Testing
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- Quartile Formula
- P Value Formula
- Skewness Formula
- R Squared Formula
- Adjusted R Squared
- Regression vs ANOVA
- Z Test Formula
- Z Score Formula
- Z Test vs T Test
- F-Test Formula
- Quantitative Research
- Histogram Examples

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## Compounding Definition

Compounding is defined as a method in which earning from capitals or fixed income is in the form of interest or capital gain, again reinvested to earn additional earning over a period of time.

Below examples of compounding helps to understand how compounding methods work and outline the potential power of compounding methods. It shows how compounding is beneficial, and longer the investment horizon the greater is the exponential growth. Let’s try to understand what is compounding and how it’s work through some basic examples

### Top 4 Examples of Power of Compounding

Let’s see some examples of power of compounding to understand it better.

#### Compounding Example #1

**Two friends Shane and Mark both decided to invest $1,00,000, but Shane decided to invest in simple interest whereas Mark invests in compound interest for 10 years at 10% interest. Let see what happens after 10 years.**

**Solution:**

So, the calculation of Shane investment will be –

**Total Earning Amount = $200,000**

With a Simple interest, Shane will get $2,00,000 after 10 years

The calculation of mark investment will be –

**Total Earning Amount = $2,59,374**

With Compound interest Mark investment values will grow to $2,59,374.

**Now Shane decided to invest through compounding method like Mark, and they both invested $2,00,000 at the rate of 15%.**

The calculation of Shane investment will be –

**Total Earning Amount = $8,09,111.55**

Shane stays invested for 10 years and gets the final amount as $8,09,111.55 at the rate of 15%.

The calculation of mark investment will be –

**Total Earning Amount = $65,83,790.52**

However, Mark is patience long-term investors and stays invested for 25 years and his investment value grows to $65,83,790.52

4.9 (1,067 ratings)

The above example shows the power of compounding, longer the investment horizon the greater is the exponential growth.

#### Compounding Example #2 (Weekly Compounding)

**Simon is having $7500 in savings and for his son’s college fund who will be going to attend the college after 15 years, he decided to invest in US Savings Bonds. Simon goal is to save $20,000 and the annual percentage rate for a US saving bond is 6%. What is the Future Value of Simon Money after 15 years?**

**Solution:**

Given,

- Principal = $7500
- Rate = 6% or 0.06
- Time Period = 15 years
- How many times it’s compounded in a year n = 52 Weeks
- Future Value =?

So, the calculation of future value will be –

The formula for weekly compounding is as below.

**F = P(1+r/n)^n*t**

- F = $7500(1+0.06/52)^52*15
- F = $7500(1+0.001153846)^780
**F = $18,437.45**

So from above calculation it is clear that Simon goal of to save $20,00 will not get achieved with above methods but it’s closer to that.

**Continuous Compounding Method –**

Now let’s try the above example with Continuous Compounding Formula.

So, the calculation of future value will be –

**F = Pe^r*t**

- F = $7500e^0.06*15
- F = $7500e^0.9
**Future Value (F)= $18,447.02**

Now even with Continuous Compounding Simon goal of savings $20,000 for his son’s college fund will not be achieved.

Let’s see with Monthly compounded Formula that how much money did Simon need to invest to achieve his goal of saving $20,000 in 15 years at with APR of 6%?

So, the calculation of future value will be –

**F = P(1+r/n)^n*t**

- $20,000 = P(1+0.06/12)^12*15
- P = $20,000/(1+0.06/12)^12*15
**Principal (P) = 8149.65**

So by Solving the above equation will get an answer that is $8,149.65 (Amount which Simon needs to invest to achieve his goal of saving $20,000 in 15 years).

#### Compounding Example #3 (Effective Annualized Yield)

**Let’s Say XYZ limited bank gives 10% per annum to Senior citizens for fixed deposit, and we assume here that bank interest is quarterly compounded like all other banks. Calculate the effective annualized yield for 5, 7 and 10 years.**

**Solution:**

##### Annualized Yield for 5 Years –

- t = 5 years
- n = 4 (quarterly compounded)
- I = 10% per annum

So A = (1+10%/100/4)^ (5*4)

- A = (1+0.025)^20
- A = 1.6386
- I = 0.6386 in 5 Years

Effective Interest = 0.6386/5

**Effective I = 12.772% Per Annum**

##### Annualized Yield for 7 Years –

- t = 7 years
- n = 4 (quarterly compounded)
- I = 10% per annum

So A = (1+10%/100/4)^ (7*4)

- A = (1+0.025)^28
- A = 1.9965
- I = 1.9965 in 7 Years
- Effective I = 0.9965/7

**Effective I = 14.236% Per Annum**

##### Annualized Yield for 10 Years –

- t = 10 years
- n = 4 (quarterly compounded)
- I = 10% per annum

So A = (1+10%/100/4)^ (10*4)

- A = (1+0.025)^40
- A = 2.685
- I = 1.685 in 10 Years
- Effective I = 1.685/10

**Effective I = 16.85% Per Annum**

#### Compounding Example #4 – (Annuities: Future Value)

**$1,000 is invested every 3 months at 4.8% per annum compounded quarterly. How much will the Annuity be worth in 10 years?**

**Solution:**

So when we say how much will the Annuity be worth in 10 years means here we have to find future value and this important because whenever there is an example on annuities we have to see what we have to find out.

So, the formula of Future Value is

**FV of Annuity = P [ (1+ r) ^{n} – 1 / r ]**

- P = Periodic Payment
- r = Rate per period
- n = Number of periods

So the formula of Future Value is

- So here P = $1,000
- r = 4.8% Per Annum or 0.048
- r (quarterly) = 0.048/4
- r (quarterly) = 0.012
- n = 10 years
- n (Number of times compounding will apply) = 10×4 =40

So, the calculation of FV of Annuity will be –

So now FV = $1000[1+0.012]^40 -1/0.012]

So by Solving the above equation will get an FV as $50,955.30

So how much will be the Annuity in 10 years and answer is **$50,955.30**

As additionally, we can also find out from the above example that how much interest is earned in 10 years.

As 40 times $1000 is invested that is a total investment (40×$1000 = $40,000).

So Interest = Future Value – Total investment

- Interest = $50,955.30 – $40,000
**Interest = $10,955.30**

So here it is important to understand that in Annuities investors can earn a lot of interest, in the above particular examples a deposit of $40,000 gives in return total interest of $10,955.30.

**Note – You can download the Excel template provided Above for detailed calculation**

### Conclusion

So the above examples show the power of the compounding method and how it helps to increase the value of assets by earning interest on both principal and accumulated interested. The first example above shows how investors can earn more money through compounding instead of simple interest method, and it tells us that patience is required to earn a higher return. The second example shows how investors can make a decision of investment by applying different methods of compounding that is Monthly, Weekly, quarterly and so on.

Compounding methods also used to compare effective Annualized Yield for different years. Example four shows how it makes investors Happy by providing higher interest return amount at the maturity of the principal. Most of the investor’s wealth is comes from compounding interest so, it important to understand the concept of compounding.

### Recommended Articles

This has been a guide to what is Compounding & its definition. Here we understand the power of compounding with the help of practical examples. You may learn more about accounting from the following articles –

- What is Compounding Formula?
- Compound Interest | Calculation with Examples
- Exponential Distribution | Definition | Examples
- Daily Compound Interest Calculation
- Compound Interest Excel Formula
- Simple Interest vs Compound Interest – Compare
- FV Excel function

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