Question

Find the amount of money that will be accumulated in a savings account If $5550 is invested at 9.0 % for 18 years and the interest is compounded continuously.Round your answer to two decimal places.

Answer 1

EXPLANATION:

We are given an investment of $5,550 that yields 9% annual interest compounded continuously.

For an investment whose interest is compounded continuously, the formula applied is;

$A=Pe^{rt}$

Where the variables are;

$\begin{gathered} A=amount\text{ after the investment period} \\ P=initial\text{ amount invested }(5550) \\ r=interest\text{ rate }(0.09) \\ t=time\text{ period in years }(18) \end{gathered}$

We can now substitute for the given values and we'll have;

$A=5550e^{0.09\times18}$

Note that the variable e is a mathematical constant whose value is approximately;

$e\approx2.7183$

We can now simplify further;

$A=5550e^^{1.62}$$A=5500(5.05309031656)$$A=27791.9967411$

We can now round this to 2 decimal places;

ANSWER:

$\begin{gathered} Amount\text{ after 18 years at 9\% compounded continuously:} \\ Amount=27,791.99 \end{gathered}$

Amount = $27,791.99