Answer :
To calculate the accrued amount of an account that compounds continuously you have to apply the following formula:
[tex]A=Pe^{rt}[/tex]Where
A is the accrued or final amount
P is the principal or initial amount
r is the interest rate expressed as a decimal value
t is the time period in years
You have to determine the principal amount given that after 9 years the final balance of an account that has an annual interest of 8% is $18,091.34
- The first step is to write the formula for the principal amount P, to do so, divide both sides of the expression by e^(rt)
[tex]\begin{gathered} \frac{A}{e^{rt}}=\frac{Pe^{rt}}{e^{rt}} \\ P=\frac{A}{e^{rt}} \end{gathered}[/tex]- Next, divide the interest rate by 100 to express it as a decimal value
[tex]\begin{gathered} r=\frac{8}{100} \\ r=0.08 \end{gathered}[/tex]- Now you can calculate the principal amount, replace the expression using A=18,091.34, r=0.08, and t=9
[tex]\begin{gathered} P=\frac{18091.34}{e^{0.08\cdot9}} \\ P=\frac{18091.34}{e^{0.72}} \\ P=8806.000558\cong8806.00 \end{gathered}[/tex]The initial amount of the investment was $8806
