Question

quiz (3.6 - 3.7)
score: 30/40 answered: 4/4
question 4
score on last try: 0 of 10 pts. see details for more.
you can retry this question below
find how much money needs to be deposited now into an account to obtain $5,700 in 12 years, if the interest rate is 4.5% per year compounded continuously.
the final amount is $
round your answer to 2 decimal places

Explanation:

Step1: Recall the formula for continuous compounding

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

Step2: Identify the values

We know that $A = 5700$, $r = 0.045$ (since $4.5\%=0.045$), and $t = 12$.

Step3: Substitute the values into the formula

First, calculate $rt$: $rt=0.045\times12 = 0.54$. Then, calculate $e^{rt}=e^{0.54}$. Using a calculator, $e^{0.54}\approx1.716003$. Then, $P=\frac{5700}{1.716003}\approx3321.67$.

Answer:

3321.67