In 2000, the balance on martins credit card increased by 40%. In 2001, the balance increased by 30%. How does the balance at the end of 2001 compare to the balance at the beginning of 2000?
To compare the balance at the end of 2001 to the balance at the beginning of 2000, we need to consider the cumulative increase over the two years.
In 2000, the balance increased by 40%. This means the balance at the beginning of 2001 would be 100% + 40% = 140% of the initial balance.
In 2001, the balance increased by an additional 30%. This means the balance at the end of 2001 would be 140% + 30% = 170% of the initial balance.
Therefore, the balance at the end of 2001 is 170% of the balance at the beginning of 2000.
To compare the balance at the end of 2001 to the balance at the beginning of 2000, we need to calculate the total increase over the two years.
1. Start with the balance at the beginning of 2000.
2. Add a 40% increase to this balance.
3. This will give you the new balance at the end of 2000.
4. Then, add a 30% increase to the balance at the end of 2000 to get the final balance at the end of 2001.
Let's calculate it step by step:
Step 1: Calculate the balance at the end of 2000.
- If the beginning balance in 2000 is B, the new balance at the end of 2000 is B + 0.40B = 1.40B.
Step 2: Calculate the balance at the end of 2001.
- If the balance at the end of 2000 is 1.40B, add a 30% increase to get the final balance at the end of 2001: 1.40B + 0.30(1.40B) = 1.82B.
Therefore, the balance at the end of 2001 is 1.82 times the balance at the beginning of 2000, or 182% of the initial balance.
To find out how the balance at the end of 2001 compares to the balance at the beginning of 2000, we need to calculate each balance separately and then compare the results.
Let's start by considering the balance at the beginning of 2000. Let's assume the initial balance is $100.
To determine the increase in 2000, we need to calculate 40% of the initial balance and then add it to the initial balance:
Increase in 2000 = 40% of $100 = (40/100) * $100 = $40
So, the new balance at the end of 2000 is $100 + $40 = $140.
Now, to determine the increase in 2001, we need to calculate 30% of the balance at the end of 2000 and add it to the balance:
Increase in 2001 = 30% of $140 = (30/100) * $140 = $42
Therefore, the balance at the end of 2001 is $140 + $42 = $182.
Comparing the balance at the end of 2001 to the balance at the beginning of 2000, we can see that the balance at the end of 2001 is $182, which is higher than the initial balance of $100.