Ohio Assessments for Educators (OAE) Mathematics Practice Exam

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What does 'r' represent in the compound interest formula P = P₀(1 + r/n)ⁿ^t?

The annual interest rate
The time in years
The initial investment amount
The total final value

The correct answer is: The annual interest rate

In the compound interest formula P = P₀(1 + r/n)ⁿ^t, 'r' represents the annual interest rate expressed as a decimal. This is a crucial component of the formula, as it determines how much interest accrues on the principal amount (P₀) over time. When calculating compound interest, the annual interest rate 'r' is divided by 'n', the number of times the interest is compounded per year, which allows the formula to account for the frequency of compounding in a given year. Understanding this concept is essential, as the rate directly impacts the growth of the investment. It essentially functions as the growth factor for the investment for each compounding period, reflecting the percentage increase in value each year due to the interest earned. This is why 'r' is vital in calculating the future value of an investment under compound interest.