Continuously Compounded Interest Word Problems Game/Worksheet

Continuously Compounded Interest Word Problems Game/Worksheet
Welcome to the Continuously Compounded Interest Word Problems Challenge! This is an interactive game designed to test your mastery over exponential growth. Instead of calculating investments that grow at fixed intervals (like monthly or quarterly), this game introduces students to the world of continuous compounding. Scroll down the page for a more detailed explanation.

 

 

How to Play

1. Extract the Core Numbers: Read the narrative prompt in the center vault. You need to pull out three specific values: the initial deposit, the annual growth rate percentage, and the duration of the investment in years.
   

2. Identify the Core Objective: Pay close attention to what the question is tracking. The simulation randomly alters its goal:
   

Accumulated Balance: The total mathematical value of the entire account at the end of the time frame.

Continuous Interest Revenue: Just the pure profit generated by the continuous growth, leaving out the original deposit.

3. Compute and Submit: Use your calculator to solve the scenario using the “PERT” formula. Input your final total into the center console box rounded to the nearest cent (two decimal places). Do not use dollar signs or separating commas.
   

4. Audit and Advance: Click Verify Financial Model. A correct calculation earns 100 for your total Portfolio Account. An incorrect submission reveals an automated math ledger breakdown highlighting exactly how the variables interact.
   

How the Math Works
When an asset compounds continuously, we use a specialized mathematical model often called the PERT formula:

A = Pe^rt

To process a problem seamlessly, map the narrative text straight to these mathematical pieces:

P (Principal): The starting amount of capital. If Logan deposits 4,500, then P = 4500.

e (Euler’s Constant): An irrational mathematical constant approximately equal to 2.71828. It naturally emerges whenever you model processes that grow continuously. On a calculator, you will use the e^x button.

r (Annual Growth Rate): The percentage rate at which the asset expands. You must convert this percentage to a decimal form before calculation (e.g., 6.25% = 0.0625).

t (Time): The total investment duration measured strictly in years.

The Order of Operations Execution
Because exponents must be handled before multiplication (PEMDAS), your calculations should always move from the top down:

1. Calculate the Exponent Factor (rt): Multiply the decimal rate by the number of years. For example, if r = 0.05 and t = 4, your exponent factor is 0.20.
   

2. Raise e to the Power: Compute e^rt on your calculator (e.g., e^0.20 ≈1.221403). This represents your asset’s total growth multiplier.
   

3. Multiply by Principal: Multiply that multiplier by your starting principal (P) to find the total continuous valuation (A).
   

4. Isolate the Goal:
   If tracking Accumulated Balance, your calculation is complete.
   If tracking Interest Revenue, subtract the initial principal from your total (A - P) to isolate the net interest gains.
   

Continuously Compounded Interest Word Problems

• Show Video

 

Check out our most popular games!
Fraction Concoction	Fact Family Game	Number Bond Garden
Online Addition Subtraction Game	Penguin Solitaire	Sawayama Solitaire
Ark Solitaire	Eldritch Invasion	Shenzhen Solitaire

Check out more Solitaire games here.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.