Question

peter is saving up money to buy a car. peter puts $6,000.00 into an account which earns 1% interest, compounded continuously. how much will he have in the account after 1 year? round your answer to the nearest cent.

Explanation:

Step1: Recall the formula for continuous compounding

The formula for continuous compounding is $A = Pe^{rt}$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal), $t$ is the time in years, and $e$ is the base of the natural logarithm.
Here, $P = 6000$, $r = 0.01$ (since 1% = 0.01), and $t = 1$.

Step2: Substitute the values into the formula

Substitute $P = 6000$, $r = 0.01$, and $t = 1$ into the formula:
$A = 6000\times e^{0.01\times1}$
$A = 6000\times e^{0.01}$

Step3: Calculate the value of $e^{0.01}$ and then multiply by 6000

We know that $e^{0.01}\approx1.010050167$ (using a calculator or the approximation of the exponential function).
Then $A = 6000\times1.010050167\approx6060.301002$

Answer:

$\$6060.30$