## Related questions with answers

Investment A offers an 8% return compounded semiannually, and Investment B offers a 7.75% return compounded continuously. Which investment has a higher rate of return over a 4-year period?

Solution

VerifiedCompound Interest Formula

$A = P\bigg(1 + \frac{r}{m}\bigg)^{mt}$

Let $P$ be the investment in both the cases. Then, the accumulated amount for investment $A$ with $r = 0.08,\ m = 2$ and $t = 4$ is

$\begin{align*} A & = P\bigg(1 + \frac{0.08}{2}\bigg)^{(2)(4)}\\ & = P(1.04)^{8}\\ & \approx 1.36857P \end{align*}$

Continuous Compound Interest Formula

$A = Pe^{rt}$

The accumulated amount for investment $B$ with $r = 0.0775$ and $t = 4$ is

$\begin{align*} A & = Pe^{(0.0775)(4)}\\ & = Pe^{0.31}\\ & \approx 1.363425P \end{align*}$

Therefore, investment $A$ has a higher rate of return.

## Create an account to view solutions

## Create an account to view solutions

## Recommended textbook solutions

#### Calculus: Early Transcendentals

7th Edition•ISBN: 9780538497909 (6 more)James Stewart#### Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

10th Edition•ISBN: 9781285464640 (4 more)Tan, Soo#### Calculus: Early Transcendentals

8th Edition•ISBN: 9781285741550 (2 more)James Stewart#### Calculus: Early Transcendentals

9th Edition•ISBN: 9781337613927 (4 more)Daniel K. Clegg, James Stewart, Saleem Watson## More related questions

- us history

1/4

- us history

1/7