The interest rate is a key factor influencing the growth of an investment with compound interest. It determines the percentage of the principal that will be added as interest in each compounding period. Higher interest rates lead to a faster growth of the investment, as more interest is earned on both the initial principal and the accumulated interest from previous periods.

In the compound interest formula \( A = P (1 + r/n)nt, the interest rate r significantly impacts the future value A of the investment. A higher interest rate means that the growth factor (1 +r/n) increases, which exponentially boosts the final amount due to the compounding effect. This exponential growth means that even small increases in the interest rate can lead to substantial differences in the investment's value over time.

For example, an investment of $1,000 compounded annually at an interest rate of 5% will grow to approximately $1,628 over 10 years. However, if the interest rate is increased to 8%, the same investment will grow to about $2,159 over the same period. This demonstrates how the interest rate magnifies the power of compounding.

Additionally, the frequency of compounding interacts with the interest rate to further affect growth. More frequent compounding periods (e.g., monthly vs. annually) result in higher overall returns, especially at higher interest rates. Therefore, the interest rate is a critical determinant of how quickly an investment grows, making it a fundamental consideration in financial planning and investment strategies.