## Related questions with answers

Use the formula for continuous compounding to compute the balance in the following accounts after $1$, $5$, and $20$ years. Also, find the $\mathrm{APY}$ for each account.

A $\$ 3000$ deposit in an account with an $\mathrm{APR}$ of $7.5 \%$

Solution

VerifiedIn the given situation, we need to determine the accumulated values of an investment of $\textcolor{#c34632}{\$3,000}$ at an interest rate of $\textcolor{#c34632}{7.5\%}$ **compounded continuously** after $\textcolor{#c34632}{1}$, $\textcolor{#c34632}{5}$, and $\textcolor{#c34632}{20}$ years.

We will use the compound interest formula for continuous compounding given by:

$A = P \times e^{(APR \times Y)}$

where $A$ is the accumulated balance after $Y$ years, $P$ is the starting principal, $APR$ is the annual percentage rate in decimal form, and $Y$ is the time in years.

Plugging in the known values, we have the following:

**After 1 year:**

$\begin{aligned} A_1 &= \$3,000 \times e^{(0.075 \times 1)} \\ &\approx \textcolor{#4257b2}{\$3,233.65} \end{aligned}$

**After 5 years:**

$\begin{aligned} A_5&= \$3,000 \times e^{(0.075 \times 5)} \\ &\approx \textcolor{#4257b2}{\$4,364.97} \end{aligned}$

**After 20 years:**

$\begin{aligned} A_{20} &= \$3,000 \times e^{(0.075 \times 20)} \\ &\approx \textcolor{#4257b2}{\$13,445.07} \end{aligned}$

## Create a free account to view solutions

## Create a free account to view solutions

## Recommended textbook solutions

#### Statistical Techniques in Business and Economics

15th Edition•ISBN: 9780073401805 (11 more)Douglas A. Lind, Samuel A. Wathen, William G. Marchal#### Using and Understanding Mathematics: A Quantitative Reasoning Approach

6th Edition•ISBN: 9780321914620Jeffrey O. Bennett, William L. Briggs#### Financial Algebra: Advanced Algebra with Financial Applications

2nd Edition•ISBN: 9781337271790Richard Sgroi, Robert Gerver## More related questions

1/4

1/7