Question

ryan invested $46,000 in an account paying an interest rate of 3.1% compounded continuously. assuming no deposits or withdrawals are made, how much money, to the nearest ten dollars, would be in the account after 7 years?

Explanation:

Step1: Recall continuous compound formula

The formula for continuous compounding is $A = Pe^{rt}$, where $P$ is principal, $r$ is annual rate, $t$ is time in years, $A$ is final amount.

Step2: Identify given values

$P = 46000$, $r = 0.031$, $t = 7$

Step3: Calculate exponent term

$rt = 0.031 \times 7 = 0.217$

Step4: Compute exponential value

$e^{0.217} \approx 1.2423$

Step5: Calculate final amount

$A = 46000 \times 1.2423 \approx 57145.8$

Step6: Round to nearest ten dollars

Round $57145.8$ to the nearest ten: $57150$

Answer:

$\$57150$