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

Step-by-step 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*18)`

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

`e\approx2.7183`

We can now simplify further;

`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