Chapter 8.2, Problem 42HP

To determine

To find: The situation when the compounding period is more frequent while the principle and rate is same.

Answer to Problem 42HP

The required solution is shown above.

Explanation of Solution

Consider the formula of compounding interest.

  $y={\left(1+\frac{i}{n}\right)}^n$

If $n$ increases and approaches $\infty$ then the value of $y$ approaches to $e^i$ .

The value of $y$ is impacted by $n$ which reduces the value of $i$ inside the parenthesis but increases the total value outside of it, forcing it to converge to the value of $e$ as $n$ gets larger and larger.

When $i$ is equal to $1$ and $y$ equal to $e$ , which is always equal to approximately $2.718$ .

Therefore, the required solution is shown above.