arturo invested $41,000 in an account paying an interest rate of 3.1% compounded continuously. assuming no…

arturo invested $41,000 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 cent, would be in the account after 18 years?

arturo invested $41,000 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 cent, would be in the account after 18 years?

Answer

Explanation:

Step1: Recall continuous - compounding formula

The formula for continuous - compounding is $A = Pe^{rt}$, where $A$ is the amount of money in the account after $t$ years, $P$ is the principal amount (initial investment), $r$ is the annual interest rate (in decimal form), and $t$ is the number of years.

Step2: Convert the interest rate to decimal

Given $r = 3.1%=0.031$, $P = 41000$, and $t = 18$.

Step3: Substitute values into the formula

$A=41000\times e^{0.031\times18}$. First, calculate the exponent: $0.031\times18 = 0.558$. Then, find $e^{0.558}$. Using a calculator, $e^{0.558}\approx1.74787$. Now, multiply by the principal: $A = 41000\times1.74787=71662.67$.

Answer:

$71662.67$