Find the principal that must be invested at the rate 6%, compounded monthly, so that $3,000,000 will be available for retirement in 55 years. Round your answer to the nearest cent.
A) $909,090.91
B) $111,563.08
C) $2,280,278.32
D) $825,000.00
E) $121,702.27

Question

Find the principal that must be invested at the rate 6%, compounded monthly, so that $3,000,000 will be available for retirement in 55 years. Round your answer to the nearest cent. ​
A) $909,090.91
B) $111,563.08
C) $2,280,278.32
D) $825,000.00
E) $121,702.27

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. Rearranging the formula to solve for $P$, we get $P = \frac{A}{(1 + \frac{r}{n})^{nt}}$. Given $A = 3,000,000$, $r = 0.06$, $n = 12$ (since the interest is compounded monthly), and $t = 55$, we can calculate the principal. Plugging these values into the formula gives the correct answer.

Find the Principal That Must Be Invested at the Rate