Question

next incorrect question
question 8 (1 point) retake question
suppose an account containing $10,742 was invested at 6.83% compounded continuously for 13 years. what was the initial deposit made into the account? round your answer to the nearest cent; do not enter the $ sign.
your answer:
box
answer

Explanation:

Step1: Recall continuous compounding formula

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

Step2: Identify values

Given $A = 10742$, $r=0.0683$ (since $6.83\%=0.0683$), and $t = 13$.

Step3: Calculate exponent

First, calculate $rt$: $rt=0.0683\times13 = 0.8879$.

Step4: Calculate $e^{rt}$

Calculate $e^{0.8879}$. Using a calculator, $e^{0.8879}\approx2.430$.

Step5: Solve for $P$

Now, $P=\frac{10742}{e^{0.8879}}\approx\frac{10742}{2.430}\approx4420.58$.

Answer:

4420.58