27 Mar Finding Real-World Examples of Exponential Functions
Part A: Finding Real-World Examples of Exponential Functions
This week you will connect the concept of exponential functions to compound interest. Watch the lecture videos below to learn about exponential functions.
Introduction to Power and Exponential Functions
Graphing Power and Exponential Functions
I have created two plots of an exponential function. This function describes how savings grow over a number of years when a fixed amount of money is deposited monthly (and there are no withdrawals!), and the interest earned is compounded.
The reason that this function is exponential in nature is because the number of years “x” over which deposits are made appears as an exponent in one of the terms. This function is essentially of the form:
y = a * bx
The link to the graph is below:
Compound Interest Plots
You need to turn the plots ON for each of the compound interest equations (lines 11 and 12 in the left-hand panel) to see the plots using the R1 and R2 rates.
In the Desmos graph, the exponential function is already programmed in. All you have to do is to set the values of interest rates for two savings accounts. All of the variables in the equation are described below. You Do Not have to calculate anything. The graph does it all for you; just read it!
P0 = amount of money you deposit each month (For simplicity, I have set this equal to 1 in the equation used in the Desmos graph. Multiply the value you will read from the y-axis in a later step, by your monthly deposit amount to get your answer in dollars).
R = interest rate over one year (APY or Annual Percentage Yield) (the interest rate should be expressed in decimal form for use in this formula, e.g. R = 0.25% = 0.0025 in decimal form). This is the only variable for which you have to set slider values.
N = number of compounding periods in one year (e.g. 12 times per year when compounding is done monthly, or 4 times per year when the compounding is done quarterly, etc.). (You will not need to change the pre-set value).
x = number of years for which the money remains invested
Read the y-value corresponding to a particular number of years. Use that y-value to multiply a recurring monthly deposit amount to find out how much money will have accrued via the compounding effect. This amount of money is also known as Future Value (FV).
Now, here is what I would like you to do:
Look up the interest rate for your savings account. The interest rate likely will be quoted as an Annual Percentage Yield (APY).
Next, look up the APY for a savings account from some other bank.
Click the link above to get to the graph I built in Desmos for the FV equation.
Use the R sliders in the graph to set the values of the APYs, one plot for each bank. (See screenshot below). Click the round buttons to the left of the Bank 1 and Bank 2 equations to turn ON the related plots.
You DO NOT need to change the values of the N sliders or to manually calculate the y-values.
Compare the plots for your two selected banks to each other and to the reference (orange) plot. Tell us what you have learned from this exercise. Please share a link to your Desmos graph (you will need to save the graph first) or provide a screenshot which includes the left-hand panel showing the interest rate values you set on the R1 and R2 sliders.Discuss your results:
Compare the plots for your two selected banks (and the reference plot) and tell us whether you were you surprised by the results?
Explain what you learned from this exercise about exponential functions and personal finance.
Here is a template for your answers. Just copy and paste the table into your own post and fill in the required values. That should make it simple and easy for you to do and for me to grade. Win, win, eh? (-:
Item Your Answers Possible Point Values
Bank 1 interest rate in % form ? 2.5/0
Bank 1 interest rate in decimal form ? 2.5/0
Bank 2 interest rate in % form ? 2.5/0
Bank 2 interest rate in decimal form ? 2.5/0
Value for the recurring deposit amount ? 2.5/0
Value for the number of years for which the deposit keeps being made ? 2.5/0
Link or screenshot to graph which must show 2 plots, one plot for Bank 1’s rate, and one plot for Bank 2’s rate(If a screenshot, it must also show left-hand panel with values of R1 and R2) Paste link here or attach screenshot to your post 5/0 for Plot 15/0 for Plot 2
Value for the growth factor for Bank 1 ? 5/0
Value for the growth factor for Bank 2 ? 5/0
Total amount accrued at Bank 1 = (recurring deposit amount * growth factor for Bank 1) ? 2.5/0
Total amount accrued at Bank 1 = (recurring deposit amount * growth factor for Bank 1) ? 2.5/0
Description of what you learned from doing this assignment. Type your answer after this table 20/14/0
Substantive Response 1 Type your answer in a response post to your classmate 20/14/0
Substantive Response 2 Type your answer in a response post to your classmate 20/14/0
Description of what you learned from doing this assignment:
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