how much should be invested now at an interest rate of 5.5% per year, compounded continuously, to have $2000…

how much should be invested now at an interest rate of 5.5% per year, compounded continuously, to have $2000 in two years? do not round any intermediate computations, and round your answer to the nearest cent. if necessary, refer to the list of financial formulas.

how much should be invested now at an interest rate of 5.5% per year, compounded continuously, to have $2000 in two years? do not round any intermediate computations, and round your answer to the nearest cent. if necessary, refer to the list of financial formulas.

Answer

Explanation:

Step1: Recall continuous - compounding formula

The formula for continuous - compounding is $A = Pe^{rt}$, where $A$ is the final amount, $P$ is the principal amount (initial investment), $r$ is the annual interest rate (in decimal form), and $t$ is the time in years. We need to solve for $P$, so we can rewrite the formula as $P=\frac{A}{e^{rt}}$.

Step2: Identify the values of $A$, $r$, and $t$

We are given that $A = 2000$, $r=0.055$ (since $5.5%=0.055$), and $t = 2$.

Step3: Substitute the values into the formula

$P=\frac{2000}{e^{0.055\times2}}=\frac{2000}{e^{0.11}}$.

Step4: Calculate the value of $P$

Using a calculator, $e^{0.11}\approx1.116278$. Then $P=\frac{2000}{1.116278}\approx1791.67$.

Answer:

$$1791.67$