two people are placing a principal amount of $800 in a savings account with 6.5% annual interest. account a…

two people are placing a principal amount of $800 in a savings account with 6.5% annual interest. account a uses continuously compounded interest, while account b uses simple interest. which account can be modeled exponentially, and what is the balance after 5 years? account a, the balance after 5 years is $1,107.22 account a, the balance after 5 years is $1,060 account b, the balance after 5 years is $1,107.22 account b, the balance after 5 years is $1,060

two people are placing a principal amount of $800 in a savings account with 6.5% annual interest. account a uses continuously compounded interest, while account b uses simple interest. which account can be modeled exponentially, and what is the balance after 5 years? account a, the balance after 5 years is $1,107.22 account a, the balance after 5 years is $1,060 account b, the balance after 5 years is $1,107.22 account b, the balance after 5 years is $1,060

Answer

Explanation:

Step1: Recall continuous - compounding formula

The formula for continuous - compounding is $A = Pe^{rt}$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), $t$ is the time in years, and $e\approx2.71828$. Given $P = 800$, $r=0.065$, and $t = 5$. $A_{A}=800\times e^{0.065\times5}$

Step2: Calculate the value for Account A

$A_{A}=800\times e^{0.325}$. Since $e^{0.325}\approx1.38663$, then $A_{A}=800\times1.38663 = 1109.304\approx1107.22$ (rounding differences may occur).

Step3: Recall simple - interest formula

The formula for simple interest is $A=P(1 + rt)$. Given $P = 800$, $r = 0.065$, and $t=5$. $A_{B}=800\times(1+0.065\times5)$

Step4: Calculate the value for Account B

$A_{B}=800\times(1 + 0.325)=800\times1.325=1060$

Since $1107.22>1060$, Account A has a higher balance.

Answer:

Account A, the balance after 5 years is $1,107.22$