enter the correct answer in the box. susanna deposits $400 in a savings account with an interest rate of 3%…
enter the correct answer in the box. susanna deposits $400 in a savings account with an interest rate of 3% compounded annually. what equation could susanna use to calculate how many years it will take for the value of the account to reach $600? fill in the values of a, b, and c to write the equation modeling this situation. $c = a(b)^x$
Answer
Explanation:
Step1: Identify the compound - interest formula components
The compound - interest formula is $c = A(b)^x$, where $c$ is the final amount, $A$ is the initial amount, $b$ is the growth factor, and $x$ is the number of time periods. The initial deposit $A = 400$, the final amount $c = 600$. The growth factor $b$ for an annual interest rate of $r$ compounded annually is $b=1 + r$. Since $r = 0.03$, then $b = 1+0.03=1.03$.
Step2: Substitute values into the formula
Substitute $A = 400$, $b = 1.03$, and $c = 600$ into the formula $c = A(b)^x$. We get $600=400(1.03)^x$.
Answer:
$A = 400$, $b = 1.03$, $c = 600$