Question

Use the equation A=Pe^rt to answer each question. Show all work.

Answer 1

the interest rate is 2.7 %

Step-by-step explanation

the continuos compound formula states that:

`\begin{gathered} A=P*e^(rt) \\ where\text{ A }is\text{ the final amount} \\ Pis\text{ the initial amount} \\ e\text{ is a math constant} \\ \text{r is the time} \end{gathered}`

so, we can isolate r

`\begin{gathered} A=Pe^(rt) \\ divide\text{ both sides by P} \\ (A)/(P)=(Pe^(rt))/(P) \\ (A)/(P)=e^(rt) \\ ln((A)/(P))=ln(e^(rt)) \\ ln((A)/(P))=rt \\ divide\text{ both sides by t} \\ (ln((A)/(P)))/(t)=(rt)/(t) \\ r=(ln((A)/(P)))/(t) \end{gathered}`

hence

Step 1

a) Let

`\begin{gathered} P=\text{ 8000} \\ A=13006.40 \\ t=\text{ 18} \end{gathered}`

b) now, replace in the formula to find the rate:

`\begin{gathered} r=(ln((A)/(P)))/(t) \\ r=(ln((13006.40)/(8000)))/(18) \\ r=(0.486)/(18) \\ r=0.027 \end{gathered}`

to get the percentage form, multiply by 100 %

`r=0.027*100\text{ \% =2.7 \%}`

so, the interest rate is 2.7 %

I hope this helps you