a principal amount of $3,150 is placed in a savings account for 19 years with an apr of 2.15%. what is the…

a principal amount of $3,150 is placed in a savings account for 19 years with an apr of 2.15%. what is the difference in the total account balances if simple interest is applied, compared to continuously compounded interest?\n$1,286.78\n$1,589.36\n$300.85\n$302.59

a principal amount of $3,150 is placed in a savings account for 19 years with an apr of 2.15%. what is the difference in the total account balances if simple interest is applied, compared to continuously compounded interest?\n$1,286.78\n$1,589.36\n$300.85\n$302.59

Answer

Explanation:

Step1: Calculate simple - interest balance

The simple - interest formula is $A = P(1+rt)$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the time in years. Given $P=$3150$, $r = 0.0215$, and $t = 19$. $A_{s}=3150\times(1 + 0.0215\times19)$ $A_{s}=3150\times(1+0.4085)$ $A_{s}=3150\times1.4085$ $A_{s}=4436.775$

Step2: Calculate continuously - compounded interest balance

The continuously - compounded interest formula is $A = Pe^{rt}$, where $e\approx2.71828$. $A_{c}=3150\times e^{0.0215\times19}$ $A_{c}=3150\times e^{0.4085}$ $A_{c}=3150\times1.50432$ $A_{c}=4738.508$

Step3: Calculate the difference

$D=A_{c}-A_{s}$ $D = 4738.508 - 4436.775$ $D = 301.733\approx302.59$

Answer:

$302.59$