Compound Interest Game

This Compound Interest Calculator Quiz and Game is a great way to put your skills to the test in a fun environment. You need to use the Compound Interest Formula to find the Future Value, Interest, Principal or Rule of 72.

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Compound Interest Game
This game focuses on the power of compounding. It covers four distinct skills:
Find Future Value (A): Using $A = P(1+r)^t$.
Find Interest (I): The difference between the Future Value and Principal (A - P).
Find Principal (P): Working backward from a target amount.
Rule of 72: A quick estimate to estimate how long it takes for money to double.
Scroll down the page for a more detailed explanation.

Compound Interest
Calculator

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How to Play the Compound Interest Game
Here’s how to play:

Start: Each Quiz consists of 10 questions. Select one of the modes: Future Value (A), Total Interest (I), Principal (P), Rule of 72.
Look at the Problem: Use the Compound Interest Formula to calculate the answer.
Select Your Answer: Select the correct answer.br>
Check Your Work: If you selected the right answer, it will be highlighted in green. If you are wrong, it will be highlighted in red and the correct answer will be highlighted in green.
Get a New Problem: Click “Next Calculation” for a new problem.
Your score is tracked, showing how many you’ve gotten right.
Finish Game When you have completed 10 questions, click “Finish Game” to get your final score.

Compound Interest Formula
Compound interest is the interest calculated on the initial principal and also on all the accumulated interest from previous periods on a deposit or loan. This process, known as “compounding,” leads to exponential growth.

The Formula
The compound interest formula calculates the Future Value of the investment or loan, not just the interest earned.
$A = P \left(1 + \frac{R}{n}\right)^{nt}$
Where:
A is the Future Value / Total Amount (The final balance after t years)
P is the Principal (The initial amount deposited or borrowed)
R is the Rate (The annual interest rate expressed as a decimal, e.g., 6% = 0.06).
t is the Time (The total duration of the investment or loan)
n is the Compounding Frequency (The number of times interest is compounded per year)

How to Use the Formula (Step-by-Step)
Step 1: Ensure Rate (R) and Time (t) are Correctly Formatted
Rate (R): Convert the percentage rate to a decimal (e.g., 5% → 0.05).
Time (t): Ensure the duration is expressed in years (e.g., 18 months → 1.5 years).
Compounding Frequency (n): Identify the correct value for n.
Step 2: Calculate the Factor Inside the Parentheses
First, calculate the interest rate per compounding period ($\frac{R}{n}$), then add 1. This represents the growth factor for a single period.
$\left(1 + \frac{R}{n}\right)$
Step 3: Calculate the Total Number of Periods
Calculate the exponent (nt), which is the total number of compounding periods over the entire duration of the loan or investment.
Step 4: Calculate the Growth Multiplier
Raise the result from Step 2 to the power of the result from Step 3. This is the total factor by which the principal will grow.
$\left(1 + \frac{R}{n}\right)^{nt}$
Step 5: Calculate the Future Value (A)
Multiply the initial Principal (P) by the growth multiplier from Step 4.
$A = P \times \left(\text{Growth Multiplier}\right)$

Example Calculation
You invest $1,000 at an annual interest rate of 6%, compounded quarterly, for 5 years. What will the total amount be after 5 years?
Given values:
P = $1,000
R = 6% = 0.06 (Decimal Rate)
t = 5 years
n = 4 (Quarterly compounding)

Plug the values into the formula:
$A = 1,000 \left(1 + \frac{0.06}{4}\right)^{(4 \times 5)}$
Simplify the terms:
$A = 1,000 \left(1 + 0.015\right)^{20}$
$A = 1,000 \left(1.015\right)^{20}$
Calculate the exponent:
$\left(1.015\right)^{20} \approx 1.346855$
Calculate the Future Value (A):
$A = 1,000 \times 1.346855$
$A \approx \$1,346.86$
The total value of the investment after 5 years will be approximately $1,346.86.
Finding the Compound Interest (I)
To find the actual amount of interest earned (I), simply subtract the Principal (P) from the Future Value (A):
I = A - P
In the example above:
I = $1,346.86 - $1,000 = $346.86

Finding the Total Interest Earned (I)
You must first calculate the final amount (A) and then subtract the initial principal (P).
The formula for total compound interest (I) is:
I = A - P
Procedure:
Calculate A using the compound interest formula:
$A = P \left(1 + \frac{R}{n}\right)^{nt}$
Calculate I by taking the final amount and subtracting the original investment (P).
Finding the Principal (P)
If you know the desired Future Value (A), the Rate (R), the Time (t), and the Compounding Frequency (n), you can find the required initial Principal (P). This is useful for answering the question: “How much must I invest today to reach a specific future goal?"
To find P, we rearrange the main formula algebraically. Since the term $\left(1 + \frac{R}{n}\right)^{nt}$ is multiplying P, we divide both sides by that term:
$P = \frac{A}{\left(1 + \frac{R}{n}\right)^{nt}}$

The Rule of 72
The Rule of 72 is a quick, easy-to-remember approximation used to estimate the number of years required to double an investment, given a fixed annual rate of return.
It provides a good estimate, especially for interest rates between 6% and 10%.
Rule of 72 Formula
$\text{Years to Double} \approx \frac{72}{\text{Annual Interest Rate (as a percentage)}}$
Important: For the Rule of 72, the annual rate is used as a whole number/percentage, not as a decimal.

Example: Using the Rule of 72
Scenario A: Finding Time
If an investment earns 9% annually, how long will it take to double your money?
$\text{Years to Double} \approx \frac{72}{9} = 8 \text{ years}$
Scenario B: Finding Rate
If you want to double your money in 6 years, what annual interest rate must you earn?
$\text{Required Rate} \approx \frac{72}{6} = 12%$

This video gives a clear, step-by-step approach to learn how to use the Compound Interest Formula.
- Show Video

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Compound Interest Game

Compound Master!