Chapter 6, Problem 2CA

To determine

To find if interest compounded continuously pays more or interest compounded daily.

Answer to Problem 2CA

The interest compounded daily amounts to more than interest compounded continuously.

Explanation of Solution

Given information:

The given statement is:

“Your friend claims more interest is earned when an account pays interest compounded continuously than when it pays interest compounded daily. Do you agree with your friend? Justify your answer.”

Calculation:

Interest compounded continuously for a year amounts to:

  $\begin{array}{l}\text{A}=\text{P}{\left(1+\frac{\text{r}}{\text{n}}\right)}^{\text{nt}}\\ \text{A}=\text{P}{\left(1+\frac{\text{r}}{\text{n}}\right)}^1\end{array}$

Interest compounded daily for a year amounts to:

  $\begin{array}{l}\text{A}=\text{P}{\left(1+\frac{\text{r}}{\text{n}}\right)}^{\text{nt}}\\ \text{A}=\text{P}{\left(1+\frac{\text{r}}{\text{365}}\right)}^{365}\end{array}$

Hence, the interest compounded daily amounts to more than interest compounded continuously.