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

The formula for compound interest is $A = P(1 + \frac{r}{n})^{nt}$, where $A$ is the amount of money accumulated after n years, including interest, $P$ is the principal amount, $r$ is the annual interest rate (decimal), $n$ is the number of times that interest is compounded per year, and $t$ is the time the money is invested for in years. We are given $A = \$1,000,000$, $r = 8\% = 0.08$, $n = 12$ (since the interest is compounded monthly), and $t = 50$ years. We need to solve for $P$. Rearranging the formula to solve for $P$, we get $P = \frac{A}{(1 + \frac{r}{n})^{nt}}$. Plugging in the given values, $P = \frac{1,000,000}{(1 + \frac{0.08}{12})^{12*50}}$, which calculates to approximately \$18,560.39.

Find the Principal That Must Be Invested at the Rate