To determine how the balance at the end of 2001 compares to the balance at the beginning of 2000, we need to account for the compound increases in Martin's credit card balance over two years.

1. First year (2000):

   • The balance increased by 40%.
   • If the balance at the beginning of 2000 is $B$, then the balance at the end of 2000 is: $B_{\text{2000 end}} = B \times (1 + 0.40) = 1.40B$

2. Second year (2001):

   • The balance increased by 20% from the end of 2000.
   • Therefore, the balance at the end of 2001 is: $B_{\text{2001 end}} = 1.40B \times (1 + 0.20) = 1.40B \times 1.20 = 1.68B$

Thus, at the end of 2001, the balance is 1.68 times the balance at the beginning of 2000. This means the balance has increased by 68%.

Conclusion:

The balance at the end of 2001 is 68% higher than the balance at the beginning of 2000.

Answer: It is 68% higher.

Would you like more details or have any other questions? Here are 5 questions to think about:

1. How does compound growth differ from simple growth?
2. What is the formula for calculating compound growth over multiple periods?
3. How would the result change if the second year's increase was compounded monthly?
4. Can you model a scenario where the balance decreases over multiple years?
5. What are real-life examples where compound growth significantly impacts finances?

Tip: When working with percentage increases over multiple periods, remember to multiply the growth factors, not add the percentages!