Final answer:
The statement about higher interest rates requiring more deposits to accumulate a given future sum is false. Higher interest rates actually result in needing fewer deposits because each deposit grows more due to compound interest.
Step-by-step explanation:
The statement that it will take longer to accumulate a future sum with a higher interest rate, holding the future value and deposit size constant, is false. In fact, the opposite is true. When the interest rate is higher, fewer deposits are needed to reach the same future sum because each deposit grows more quickly thanks to the power of compound interest.
For example, if you need to accumulate $1,000 and make a $100 deposit annually at a 5% interest rate, it will take fewer years to reach $1,000 than if you had a 2% interest rate. Although the actual dollar amount of the deposits remains constant, the future value of these deposits increases at a faster rate when the interest rate goes up. This demonstrates the significant effect of interest rates on investment growth and savings over time.