Question

If you put $5,000 in a savings account that pays simple interest at 3.5% annually, which statement BEST describes how the account grows? Responses A linear growth, because the account grows by a constant ratelinear growth, because the account grows by a constant rate B exponential growth, because the account grows by a constant rateexponential growth, because the account grows by a constant rate C linear growth, because the account grows by a constant proportionlinear growth, because the account grows by a constant proportion D exponential growth, because the account grows by a constant proportion

Answer 1

The correct answer is D: exponential growth, because the account grows by a constant proportion.

When money is invested in a savings account that pays simple interest, the interest earned is calculated based on the initial principal amount and does not compound over time. In this case, the $5,000 initial investment will earn 3.5% interest annually. This means that every year, the account will grow by 3.5% of the initial principal amount.

To understand why this growth is exponential rather than linear, let's consider an example. In the first year, the account will earn $5,000 * 0.035 = $175 in interest. Therefore, at the end of the first year, the total amount in the account will be $5,000 + $175 = $5,175.

In the second year, the interest earned will be calculated based on the new total amount of $5,175. Therefore, the interest earned in the second year will be $5,175 * 0.035 = $181.13 (rounded to two decimal places). Adding this interest to the total amount gives us $5,175 + $181.13 = $5,356.13.

As we can see from this example, each year's interest is calculated based on the new total amount in the account. This means that as time goes on, the interest earned increases because it is calculated based on a larger principal amount. Consequently, the growth of the account is exponential rather than linear.

To further illustrate this point, let's calculate the total amount in the account after five years:

Year 1: $5,000 + ($5,000 * 0.035) = $5,175

Year 2: $5,175 + ($5,175 * 0.035) = $5,356.13

Year 3: $5,356.13 + ($5,356.13 * 0.035) = $5,545.89

Year 4: $5,545.89 + ($5,545.89 * 0.035) = $5,744.09

Year 5: $5,744.09 + ($5,744.09 * 0.035) = $5,951.22

As we can see from this calculation, the growth of the account is not linear but rather exponential. The total amount in the account increases at an increasing rate each year.

In summary, when $5,000 is invested in a savings account that pays simple interest at 3.5% annually, the account grows exponentially because the interest earned is calculated based on the new total amount each year.

Explanation: