You have to find how much money they should invest to have a balance of $7500 after eleven years, given that the account compounds continuously with a yearly interest rate of 9%.
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.
e is the natural number.
r is the interest rate expressed as a decimal value.
t is the time period expressed in years.
To calculate the initial amount P, first write the equation for the variable you want to study:
[tex]\begin{gathered} A=Pe^{rt} \\ Divide\text{ }by\text{ }e^{rt} \\ \frac{A}{e^{rt}}=\frac{Pe^{rt}}{e^{rt}} \\ \frac{A}{e^{rt}}=P \end{gathered}[/tex]- Divide the interest rate by 100 to express it as a decimal value:
[tex]\begin{gathered} r=\frac{R}{100} \\ r=\frac{9}{100} \\ r=0.09 \end{gathered}[/tex]Using A=7500, r=0.09 and t=11 calculate the initial amount P:
[tex]\begin{gathered} P=\frac{A}{e^{rt}} \\ P=\frac{7500}{e^{0.09*11}} \\ P=\frac{7500}{e^{0.99}} \\ P=2786.825\cong2786.83 \end{gathered}[/tex]Mr. and Ms. Kim have to invest $2,786.83 to be able to contribute $7,500 to their daughter's education.
