Compounding vs. Speculation

This tool performs four features.

First, it allows you to compare a fixed rate of return to a volatile rate of return.  To do this, just change the next to last speculative interest rate (in column 3 of the spreadsheet) to minus 50%.  It is not critical in which year(s) you place the minus return(s).  The nearer it is to the end, the more impact (more negative) it will have.  Of course, the minus 50% is an arbitrary amount of loss, you may also use any negative rate of return.  Click the graph button for a visual demonstration.

Second, it allows you to demonstrate the growth of a lump sum at two different series of rates of return.  For example, you might compare the growth of $100,000 at the following growth rates:

Year        Rate of Return 1                Rate of Return 2

1                10%                                 8%

2                 5%                                12%

3                 6%                                 6%

4                12%                                14%

5                 7%                                 9%

To find the answer, you would enter $100,000, 10%, and 5 years on the input screen.  Then click calculate.  Then edit the left column of interest rates (from 10%) to the rates shown in the left column above.  Then edit the right column of interest rates (from 10%) to the rates shown in the right column above.  The results appear in the bottom row.

Third, by clicking the Shuffle button, you can demonstrate that the order of returns does not change the final dollar balance of an investment (assuming no contributions or withdrawals).  Clicking the Shuffle button arranges the speculative rates of return randomly.  For example, if you invest $1,000 for three years and the rates of return for each year are:

Year 1                10%

Year 2                11%

Year 3                12%

After three years, you will have $ 1,367.52.

However, if the returns are in this order:

Year 1                12%

Year 2                11%

Year 3                10%

After three years, you will still have $ 1,367.52.

That is, the order of the returns makes no difference on the final dollar value.

Finally, clicking the Questions button will display allow you to demonstrate how difficult (or how long it takes) it is to recover from a large loss.

No example script available for this screen.

Assumptions:

•All payments are at beginning of year

•Compounding annually.

This tool uses the following simple math calculation.

Compounding Rate is one plus the interest rate for compounding or speculation. In equation form, the compounding rate for the compounding scenario is:

compounding rate = (1 + Comp ROR).

and for the speculative scenario is:

speculative rate = (1 + Spec ROR).

For both the compounding and speculation scenarios:

Balance at End of Year = Balance at Beginning of Year * (1 + Rate of Return).

The difference is calculated as:

Difference = Compounding Balance at End of Year - Speculation Balance at End of Year

Shuffle Button

Clicking the Shuffle Button arranges the Speculative rates of return randomly.  It demonstrates that the order of rate of return has no impact on the final dollar value.  The year-by-year balance calculations do not change.

Questions Button

Standard financial time value of money calculations are performed to solve the two loss recovery questions.

Question One:

What rate of return would the speculation account need to recovery to the pre-loss compounding balance (in the last row of column 2)?

Required Rate = RATE(Years Left to Recover, 0, Current Speculative Balance at End of Year, Final Compounding Balance Target)

Question Two:

Assuming your account returns ____ per year, which is your highest speculative return prior to the last year of negative returns, how long will it take to return your account to your pre-loss compounding balance (in the last row of column 2)?"

Number of Years = NPER(Highest Pre-Loss ROR, 0, Current Speculative Balance at End of Year, Final Compounding Balance Target)