Pre-Algebra
Personal financial literacy
Compound interest
20 practice questions
0 video lessons
Theory + worked examples
Compound Interest
Texas Pre-Algebra (TEKS) • Standard 8.12(D) • Financial Literacy
Compound Interest is a topic in Financial Literacy in the Texas Essential Knowledge and Skills. It is aligned to Standard 8.12(D), which requires students to calculate compound interest and compare it with simple interest.
Compound interest earns interest on both principal and previously earned interest, growing faster than simple interest.
Theory
Compound interest earns interest on the principal and on interest already earned.
Yearly compounding: \(A=P(1+r)^t\), which outgrows simple interest over time.
Compound grows faster than simple.
Compound interest.
Compound amount (yearly):
\[A=P(1+r)^t\]
Interest on interest is the key idea.
How to find compound interest
- Write the rate as a decimal.
- Use \(A=P(1+r)^t\) for yearly compounding.
- Subtract the principal for the interest earned.
- Compare with simple interest.
Example 1 β One year
\(\$100\) at \(10\%\) compounded yearly. After \(1\) year?
Solution
Multiply by \(1.10\).
| \(100\cdot1.10\) | \(=\) | \(\$110\) |
Example 2 β Two years
After \(2\) years?
Solution
Interest on interest.
| \(100\cdot1.10^2\) | \(=\) | \(\$121\) |
Example 3 β Formula
\(\$500\) at \(4\%\) for \(3\) years, compounded yearly.
Solution
Use \(A=P(1+r)^t\).
| \(500(1.04)^3\) | \(\approx\) | \(\$562.43\) |
Example 4 β vs simple
Why does compound beat simple interest?
Solution
It earns interest on previously earned interest.
Common pitfalls
Compound uses an exponent \(t\), not multiplication by \(t\).
Interest earns interest β that is the difference.
Convert the rate to a decimal.
Frequently asked questions
What is compound interest?
Interest earned on principal and prior interest.
What is the yearly formula?
\(A=P(1+r)^t\).
Does it beat simple interest?
Yes, over time.
$100 at 10% for 2 years compounded?
\(\$121\).
β Previous subtopic
Comparing salaries and lifetime income
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Cost of credit and loan repayment
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