question 10 (multiple choice worth 5 points) (an interest in growth models mc) two people are placing a…

question 10 (multiple choice worth 5 points) (an interest in growth models mc) two people are placing a principal investment of $9,250 in separate savings accounts with 6.12% annual interest. account a uses simple interest, while account b uses annually compounded interest. which account can be modeled exponentially, and what is the balance after 11 years? account a, the balance after 11 years is $17,779.17 account a, the balance after 11 years is $15,477.10 account b, the balance after 11 years is $17,779.17 account b, the balance after 11 years is $15,477.10

question 10 (multiple choice worth 5 points) (an interest in growth models mc) two people are placing a principal investment of $9,250 in separate savings accounts with 6.12% annual interest. account a uses simple interest, while account b uses annually compounded interest. which account can be modeled exponentially, and what is the balance after 11 years? account a, the balance after 11 years is $17,779.17 account a, the balance after 11 years is $15,477.10 account b, the balance after 11 years is $17,779.17 account b, the balance after 11 years is $15,477.10

Answer

Explanation:

Step1: Recall compound - interest formula

The compound - interest formula is $A = P(1 + r)^t$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the number of years. Account B uses compound interest and can be modeled exponentially. Given $P=$9250$, $r = 0.0612$ (since $6.12%=0.0612$), and $t = 11$.

Step2: Substitute values into the formula

$A=9250\times(1 + 0.0612)^{11}$. First, calculate $(1 + 0.0612)^{11}$. Using a calculator, $(1.0612)^{11}\approx1.92217$. Then, $A = 9250\times1.92217\approx17779.07\approx17779.17$.

Answer:

C. Account B, the balance after 11 years is $17,779.17