Question

Solve the problem down below. Round to the nearest cent.Don’t round until the final answer

Answer 1

The continuous compound interest is expressed as

`\begin{gathered} P(t)=P_0* e^(rt) \\ where \\ P(t)=value\text{ at time t} \\ P_0=principal\text{ amount} \\ r=annual\text{ interest rate} \\ t=length\text{ of time the interest is applied} \end{gathered}`

Given that

`\begin{gathered} t=6 \\ r=3.5\%=0.035 \\ P_0=\$16000 \end{gathered}`

By substitution, we have

`\begin{gathered} P(t)=16000* e^((0.035*6)) \\ =19738.84895 \\ \Rightarrow P(t)\approx\$19738.8\text{ \lparen nearest cent\rparen} \end{gathered}`

Hence, we have