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Mr. and Mrs. Williams hope to send their daughter to college in thirteen years. How much money should they invest now at an interest rate of
9% per year, compounded continuously, in order to be able to contribute
$9500 to her education?
Do not round any intermediate computations, and round your answer to the nearest cent.

$◻

Mr. and Mrs. Williams hope to send their daughter to college in thirteen years. How much money should they invest now at an interest rate of $9 \%$ per year, compounded continuously, in order to be able to contribute $\$ 9500$ to her education? $\newline$ Do not round any intermediate computations, and round your answer to the nearest cent. $\newline$ \($\) _____

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Exponential growth and decay: word problems

Full solution

Q. Mr. and Mrs. Williams hope to send their daughter to college in thirteen years. How much money should they invest now at an interest rate of

9 \%

per year, compounded continuously, in order to be able to contribute

\$ 9500

to her education?

\newline

Do not round any intermediate computations, and round your answer to the nearest cent.

\newline

\($\) _____

Identify formula: Identify the formula for continuous compounding: $P = Pe^{rt}$ where $P$ is the future value, $P_0$ is the initial investment, $r$ is the interest rate, and $t$ is the time in years.
Set up equation: Set up the equation with the given values: $9500 = P_0 \times e^{0.09 \times 13}$ .
Calculate value: Calculate $e^{0.09 \times 13}$ using a calculator: $e^{1.17} \approx 3.22$ .
Solve for P $0$ : Solve for $P_0$ by dividing both sides by $3$ . $22$ : $P_0 = \frac{9500}{3.22}$ .
Perform division: Perform the division to find $P_0$ : $P_0 \approx 2950.31$ .

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