find the present value of the deposit. $34,000 at 4.9% compounded continuously for 9 years. the present…

Explanation:

Step1: Recall continuous - compounding formula

The formula for continuous compounding is $A = Pe^{rt}$, where $A$ is the future value, $P$ is the present value, $r$ is the annual interest rate (in decimal form), and $t$ is the number of years. We want to find $P$, so we can rewrite the formula as $P=\frac{A}{e^{rt}}$.

Step2: Convert the interest rate to decimal

The annual interest rate $r = 4.9%=0.049$, $A = 34000$, and $t = 9$.

Step3: Substitute the values into the formula

$P=\frac{34000}{e^{0.049\times9}}$. First, calculate the exponent: $0.049\times9 = 0.441$. Then, find $e^{0.441}\approx1.55497$. $P=\frac{34000}{1.55497}\approx21865.34$.

Answer:

$21865.34$