Money in a bank account that compounds interest by some percentage acts______.
a. linearly
b. exponentially
c. negatively
d. like a fraction
B?
Does the formula have an exponent in it? If so, yes.
yes, b.
Thank you.
Yes, the correct answer is b. exponentially.
To understand why money in a bank account that compounds interest acts exponentially, let's break it down:
When money compounds interest, it means that the interest is added to the initial investment, and then that new total becomes the base for calculating the next round of interest. In other words, the interest earned in each period is added to the principal, and then interest is calculated on the new total.
This compounding process creates exponential growth because each period builds upon the previous one. As the interest is reinvested, it generates additional results, leading to an accelerated growth rate over time.
For example, if you have $1,000 in a bank account with an annual interest rate of 5% that compounds annually, at the end of the first year, you would earn $50 in interest, resulting in a total balance of $1,050. In the second year, you would earn interest on the new total of $1,050, which would be $52.50, increasing the balance to $1,102.50. The interest continues to compound and increase the balance exponentially over time.
Therefore, money in a bank account that compounds interest acts exponentially, which is why option b is the correct answer.