Final answer:
A 1% interest rate would c. reduce the impact of compounding, as compounding is more effective with higher interest rates. An initial investment's growth is significantly lesser at a 1% rate compared to higher rates, which is exemplified when contrasting 1% with hypothetical rates of 4% and 5%.
Step-by-step explanation:
When it comes to the impact of a low interest rate on the power of compounding, a 1% interest rate would c. reduce the impact of compounding. Compounding is most powerful when the interest rate is higher, as the interest earned on both the initial principal and the accumulated interest from previous periods can grow significantly over time. At a lower interest rate like 1%, the growth of the investment due to compounding will be less dramatic compared to higher interest rates.
For example, using the formula for compound interest, you can see that an initial investment of $3,000 with a 7% annual rate of return, compounded over 40 years, would grow to $44,923. However, with a 1% annual rate of return, the growth would be much more modest. Compound interest and compound growth rates behave in the same way as productivity rates—small changes in the interest rate can have significant impacts on the final amount over an extended period due to the compounding effect.
To illustrate this difference further, if we compare the result of a 1% interest rate to hypothetical rates of 4% and 5%, it becomes clear that the higher rates would lead to a more significant accumulation of wealth, thereby demonstrating how sensitive the accumulation is to the interest rate.