Answer
$$P = \$ 224,174.48$$
Work Step by Step
$$\eqalign{
& r = 7\frac{1}{2}\% ,{\text{ }}t = 20 \cr
& {\text{The formula for the amount }}A{\text{ in a savings account }} \cr
& {\text{compounded }}n{\text{ times per year for }}t{\text{ years at an interest }} \cr
& {\text{rate }}r{\text{ and an initial deposit of }}P{\text{ is given by}} \cr
& A = P{\left( {1 + \frac{r}{n}} \right)^{nt}}{\text{ }}\left( {\bf{1}} \right) \cr
& {\text{From the given information:}} \cr
& A = 1,000,000,{\text{ }}r = 7\frac{1}{2}\% = 0.075,{\text{ }}n = 12\left( {{\text{a year}}} \right),{\text{ }}t = 20 \cr
& {\text{Substituting these values into }}\left( {\bf{1}} \right) \cr
& \$ 1,000,000 = P{\left( {1 + \frac{{0.075}}{{12}}} \right)^{\left( {12} \right)\left( {20} \right)}} \cr
& {\text{Simplifying}} \cr
& \$ 1,000,000\$ = P{\left( {1.00625} \right)^{240}} \cr
& {\text{Solve for }}P \cr
& \frac{{\$ 1,000,000}}{{{{\left( {1.00625} \right)}^{240}}}} = P \cr
& P = \$ 224,174.48 \cr} $$
