A few interesting things

In class the other day, I decided to further test the idea that compounding interest annually, monthly, daily, and continuously will continue to yield large differences in the amount of interest earned. In short, I found that for a significant interest rate, there is a significant difference in the final amount in the account after 50 years. I define a significant interest rate as above 3%, as this is the point at which the difference between compounding continuously and compounding monthly is above $100. At rates below this, after 50 years the difference is less that $100.

My findings show that unless you have an interest rate about 5%, and you keep your money in the bank for over 50 years, the difference between the different final amounts is not very significant. You might make an extra $10 in 50 years if you compound continuously instead of monthly, but lets be honest, you aren't likely to make a savings account for much more than 50 years.

If you want to see my process for finding this, I will post the process below, including screen shots.

I did this by using Microsof Excel as a calculator, inserting the correct equations, and auto filling own to 50 years.

I will walk you through how to do this, and then you can try it too!

First I made two columns. The first, column A, was titled "Number of Years" and the second, column B, "Interest Rate." I auto filled

the numbers 1-100 in column A, and entered the number .02 in column

B to represent a 2% interest rate.

*Note: To make this easier to fit in a blog post, i skipped over the numbers 6-50 and 51-100.

I then made four more columns with the headings Continuous, Daily, Monthly, and Yearly. This is only to show which compounding period is being used.

Then I entered the compound interest formula in column C, compounded continuously. To do this, I entered this equation into cell C2: =5000*exp(B$2*A2) In the equation, exp() tells the computer to use the constant e and raise it to an exponent. I then used auto fill to fill in the rest of the cells with this formula.

I then entered the equation =5000*(1+(b$2/365))^(365*a2) in cell D2, under the heading Daily. This formula is the compound interest formula. I did the same thing in the next two. columns, but used the formula for monthly and yearly.

I used 4 decimal places as in some of the examples it is not possible to see a difference with just 2 decimal places.

Because of how these equations are set up, if you change the number in cell b2, you change all of the equation. If you instruct excel to use a specific cell, in this case B2, adding a dollar sign to the cell name in the equation will make that cell a constant. That way, auto fill will always use the same cell in the equation.

There is another, simpler way to calculate this. It is called the rule of 72. If you take you interest rate and divide it out of 72, you will get the number of years that it should take any amount of money under that rate to double. It is not exact, but it works. This is generally used for non continuous compounding, and is used as a rough estimate.

In this case, it should take 36 years for any amount of money deposited to double at a rate of 2%.

I hope you find this interesting.

Marc