In 2000, the balance on Martin’s 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 on 2000? In percentage form
To find the final balance at the end of 2001, we need to multiply the balance at the beginning of 2000 by 1 + 0.4 to account for the increase in 2000.
Then, we need to multiply the result by 1 + 0.3 to account for the increase in 2001.
So, the balance at the end of 2001 is (1 + 0.4) * (1 + 0.3) times the balance at the beginning of 2000.
In percentage form, this can be simplified as follows:
[(1 + 0.4) * (1 + 0.3) - 1] * 100
= (1.4 * 1.3 - 1) * 100
= 1.82 * 100
= 182%
Therefore, the balance at the end of 2001 is 182% of the balance at the beginning of 2000.
To find out how the balance at the end of 2001 compares to the balance at the beginning of 2000 in percentage form, you can calculate the total percentage increase.
First, let's assume the initial balance at the beginning of 2000 is 100 units.
In 2000, the balance increased by 40%, so the new balance at the end of 2000 would be:
Initial balance + (Increase percentage × Initial balance)
= 100 + (40% × 100)
= 100 + (0.4 × 100)
= 100 + 40
= 140
In 2001, the balance increased by 30%, so the new balance at the end of 2001 would be:
Previous balance at the end of 2000 + (Increase percentage × Previous balance)
= 140 + (30% × 140)
= 140 + (0.3 × 140)
= 140 + 42
= 182
The balance at the end of 2001 (182 units) is therefore 182% of the initial balance at the beginning of 2000 (100 units).
So, the balance at the end of 2001 is 182% 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 in percentage form, we need to calculate the final balance and then find the percentage increase.
Let's assume the balance at the beginning of 2000 is $100.
In 2000, the balance increased by 40%. To find the new balance, we multiply the initial balance by 1 plus the percentage increase: $100 * (1 + 0.40) = $140.
In 2001, the balance increased by 30%. Again, we multiply the previous balance by 1 plus the percentage increase: $140 * (1 + 0.30) = $182.
To find the percentage change, we take the difference between the final balance and the initial balance, divide it by the initial balance, and then multiply by 100: ($182 - $100) / $100 * 100 = 82%.
Therefore, the balance at the end of 2001 is 82% higher than the balance at the beginning of 2000.