14 Math Basics for Financial Literacy
Learning Outcomes:
- Define percentage and discover its relationship to fractions and decimals.
- Learn and use the 1% Math Trick and the Rule of 72.
- Solve basic percentage problems related to financial literacy.
Introduction
Understanding percentages is one of the most important math skills you will use to achieve financial literacy. You will see percentages discussed with regard to interest rates for loans, credit cards, fixed savings, and investment accounts.
Percentage is defined as a number that is a ratio. It can be described as a part of a whole. The whole may be represented as hundred (100) or one (1.00). Simply, the word percent means “out of each hundred” or “per one hundred”. To determine a percentage, divide the part by the whole and then multiply the result by 100.
For example, 1/8 = 1 ÷ 8 = 0.125 = 0.125 ×100 = 12.5%
The Percent-Fraction-Decimal Relationship
Percents, fractions, and decimals are interrelated.
To convert percent to a fraction, eliminate the percentage (%) sign and divide the number by 100. Then reduce the fraction, if necessary.
Examples:
1% = 1/100
10% = 10/100 = 1/10
100% = 100/100 = 1
250% = 250/100 = 25/10 = 5/2
To convert percent to decimal, move the decimal point 2 places to the left and eliminate the percentage (%) sign.
Examples:
1% = .01
10% = .10
100% = 1.00
250% = 2.50
Chart of Common Conversions
|
Percent |
Fraction |
Decimal |
|
25% |
1/4 |
.25 |
|
50% |
1/2 |
.50 |
|
75% |
3/4 |
.75 |
|
20% |
1/5 |
.20 |
|
40% |
2/5 |
.40 |
|
60% |
3/5 |
.60 |
|
80% |
4/5 |
.80 |
|
33 1/3 % |
1/3 |
.333 |
|
66 2/3 % |
2/3 |
.666 |
|
12 ½ % |
1/8 |
.125 |
|
37 ½ % |
3/8 |
.375 |
|
62 ½ % |
5/8 |
.625 |
|
87 ½ % |
7/8 |
.875 |
|
10% |
1/10 |
.10 |
The 1% Trick
The 1% Trick involves moving the decimal point of a number two places to the left.
For example, 1% of 500 = 5.
All whole numbers are understood to have a decimal point at the end of the number. So, 500 can be written as 500.0 or 500.00. Moving the decimal two places to the left can result in 5.000 or 5.0000 or simply 5.
Watch this video:
For the 1% trick and alternative methods to calculate percents, view this video:
Simple Interest
To calculate simple interest (I), just multiply the loan principal (P) by the interest rate (r) by the term (t) of the loan. Principal is the amount of money you deposit or borrow. Interest rate is the percentage paid for depositing your money or the percentage charged by lender for borrowing money. Term refers to the fixed or limited period of time for the loan; usually noted in years.
The formula is written as: I = P × r × t
where
r = interest rate
Example:
Riley deposits $100 into a savings account that earns 4% interest per year. How much money will they have after 5 years? Answer = $120.00
Simple Interest = 100×0.04×5= 20
Principal plus interest after 5 years = $100 + $20 = $120.00
View this video for summary and practice:
Compound Interest
Compound interest is more complex to calculate than simple interest. Compound Interest is the interest calculated on the initial principal plus previously accumulated interest.
The formula for calculating the total amount paid out is written as: [Equation]
where
Example:
Riley deposits $100 into a savings account that earns 4% interest per year compounded. How much money will they have after 5 years? Answer = $121.67
n = 1
t = 5
A = P (1 + r/n)nt
A = 100 (1 + 4%/1)1 × 5
A = 100 (1 + 0.04)5
A = 121.67
View this video to see the difference between simple and compound interest:
As a saver or as a borrower, it is important to know that most interest is compounded over time.
Want more practice on your own? Check out the Percent chapter in the Prealgebra textbook, accessible for free at https://openstax.org/books/prealgebra-2e/pages/1-introduction (Marecek et al., 2020).
The Rule of 72
The Rule of 72 is a simplified version of calculating compound interest. It is a quick and useful tool that you can use to estimate the number of years required to double an investment at a given annual interest rate. Alternatively, you can estimate the required annual interest rate to double an investment.
However, you should be aware that the Rule of 72 is most accurate for the range of interest rates between 6% to 10% (Kenton, 2024).
To calculate the number of years to double an investment, use the Rule of 72 formula:
Example:
If you initially invest $100 at an annual interest rate of 5%, how long will it take to double this investment?
So, it will take over 14 years to double your initial investment.
Looking for an online Rule of 72 calculator? Check this out!
Please Provide Feedback
What is one tip that you learned from this chapter?
References:
Furey, Edward (2024, March 27). Rule of 72 Calculator. CalculatorSoup.
https://www.calculatorsoup.com/calculators/financial/rule-of-72-calculator.php
Kenton, Will. (2024, May 31) The Rule of 72: Definition, Usefulness, and How to Use It. Investopedia. https://www.investopedia.com/terms/r/ruleof72.asp#toc-who- came-up-with-the-rule-of-72
Marecek, L., Anthony-Smith, M., & Honeycutt Mattis, A. (2020). Prealgebra 2e. OpenStax. https://openstax.org/books/prealgebra-2e/pages/1-introduction
