Find the principal that must be invested at the rate 8%, compounded monthly, so that $1,000,000 will be available for retirement in 50 years.Round your answer to the nearest cent.
A)$250,000.00
B)$18,560.39
C)$717,324.37
D)$333,333.33
E)$21,321.23

Question

Quizplus · Accepted Answer

To find the principal (P) that must be invested to grow to a future value (A) at an interest rate (r) compounded n times per year for t years, we use the formula: $A = P(1 + \frac{r}{n})^{nt}$. Here, $A = \$1,000,000$, $r = 0.08$ (8% as a decimal), $n = 12$ (compounded monthly), and $t = 50$ years. Rearranging the formula to solve for P gives $P = \frac{A}{(1 + \frac{r}{n})^{nt}}$. Substituting the given values and solving for P gives $P = \frac{\$1,000,000}{(1 + \frac{0.08}{12})^{12*50}}$, which calculates to approximately \$18,560.39.

Find the Principal That Must Be Invested at the Rate