Simple interest and Compound Interest  SAT Math Part 35  Summary and Q&A
TL;DR
James will have approximately $10,071.35 more in his account compared to Rebecca after a 20year period due to the compound effect of interest.
Questions & Answers
Q: What is the difference between simple interest and compound interest?
Simple interest is calculated only on the initial investment, while compound interest is calculated on both the initial investment and the accumulated interest.
Q: How does compound interest affect the growth of an investment compared to simple interest?
Compound interest allows for interest to be earned on both the principal and the interest accumulated in past years, leading to exponential growth in the investment over time.
Q: What role does the interest rate play in determining the final amount in an investment account?
A higher interest rate leads to greater growth in the investment over time. Even a small difference in interest rates, such as 3%, can result in a significant difference in the final amount.
Q: How does the frequency of compounding impact the growth of an investment account?
More frequent compounding, such as monthly compared to semiannually, leads to higher growth in the investment. Increasing the number of compounding periods in a year increases the account value.
Summary & Key Takeaways

Rebecca invests $10,000 in an account with a 6% annual simple interest rate, earning $600 in interest each year for 20 years, totaling $12,000.

James also invests $10,000, but in an account with a 6% annual compound interest rate. After 20 years, he will have $32,071.35, tripling his initial investment.

Austin invests $10,000 with a 9% annual compound interest rate, and Rachel invests the same amount with a 12% annual compound interest rate. After 20 years, Rachel will have approximately $47,107.46 more in her account compared to Austin.