Question

Find the amount that results from the given investment.$10 invested at 10% compounded continuously after a period of 3 yearsAfter 3 years, the investment results in $(Round to the nearest cent as needed.)

Answer 1

The continuous compound interest formula is expressed as

`\begin{gathered} A=P* e^(rt) \\ where \\ A\Rightarrow final\text{ amount} \\ P\Rightarrow initial\text{ investment} \\ e\Rightarrow Napier^(\prime)sNumber≅2.7183 \\ r\Rightarrow interest\text{ rate} \\ t\Rightarrow time \end{gathered}`

Given that $10 is invested at 10% compounded continuously after a period of 3 years, this implies that

`\begin{gathered} P=10 \\ r=10\%\text{=0.1} \\ t=3\text{ } \end{gathered}`

The amount that results from the investment is evaluated by substituting these above values into the equation.

Thus,

`\begin{gathered} A=10*(\text{2.7183\rparen}^{(0.1*\text{3\rparen}} \\ =10*(2.7183)^(0.3) \\ =10*\text{1.349861515} \\ =13.49861515 \\ \Rightarrow A\approx\$\text{13.5 \lparen nearest cent\rparen} \end{gathered}`

Hence, the amount that results from the investment is evaluated to be $13.5 (nearest cent).