Question

I REALLY NEED HELP!

Use the continuous change function A(t) = Pe^rt to answer the question.

You invest $3,700 in an account that grows 4.5% each year. What will be your investment amount after 7 years?

A.
$4,795.91

B.
$4,895.58

C.
$5,069.96

D.
$5,250.55

Answer 1

`\bf ~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^(rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$3700\\ r=rate\to 4.5\%\to (4.5)/(100)\dotfill &0.045\\ t=years\dotfill &7 \end{cases} \\\\\\ A=3700e^(0.045\cdot 7)\implies A=3700e^(0.315)\implies A\approx 5069.96`

Answer 2

C. $5,069.96

Explanation:

You are given ...

• P = 3700
• r = 0.045
• t = 7

Put these values in the formula where the corresponding variable is, then do the arithmetic.

... A = 3700·e^(0.045·7)

... = 3700·e^0.315

... ≈ 3700·1.3702593

... ≈ 5069.9594...

The balance will be $5069.96.