Determine the principal P (to the nearest cent)that will yield a balance of $A = 2,500,000$ dollars when invested at rate $r = 10 \%$ for 40 years, compounded 365 times per year. Round the answer to two decimal places.
A)$38,920.73
B)$1,541,095.89
C)$1,712.33
D)$2,472,756.03
E)$45,814.19

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. Rearranging the formula to solve for $P$, we get $P = \frac{A}{(1 + \frac{r}{n})^{nt}}$. Substituting $A = 2,500,000$, $r = 0.10$, $n = 365$, and $t = 40$ into the formula, we calculate $P$ to be approximately $45,814.19.

Determine the Principal P (To the Nearest Cent)that Will Yield A=2,500,000A = 2,500,000A=2,500,000

Determine the Principal P (To the Nearest Cent)that Will Yield $A = 2,500,000$