Answer
\[\$28,469.44\].
Work Step by Step
Calculation of principal amount of deposit can be done by using formula:
\[P=\frac{A}{{{\left( 1+\frac{r}{n} \right)}^{nt}}}\]
Where A denotes the Future value of the loan, P denotes the Principal amount, R denotes the rate of interest, t denotes the number of years and n denotes the number of times compounding is done in a year.
Compute the principal amount by substituting the values in the formula as mentioned below:
\[\begin{align}
& P=\frac{A}{{{\left( 1+\frac{r}{n} \right)}^{nt}}} \\
& =\frac{\$100,000}{{{\left(1+\frac{0.07}{12}\right)}^{12\times18}}}\end{align}\]
Solve and simplify the equation as follows:
\[\begin{align}
& P=\frac{\$100,000}{{{\left(1+0.005833\right)}^{216}}}\\&=\frac{\$100,000}{{{\left(1.005833\right)}^{216}}}\\&=\frac{\$100,000}{3.512539}\\&=\$28,469.44\end{align}\]
Hence, the amount deposited by the parents for a college education is\[\$28,469.44\].
