Question

Jessica opened a bank account that earns $2$ percent interest compounded annually. Her initial deposit was 100$,andsheusestheexpression$ $100{\left(x\right)}^t$ to find the value of the account after $t$ years.
What is the value of $x$ in the expression?

• A. 1.01
• B. 1.02
• C. 1.03
• D. 1.2

Answer 1

The correct option is B 1.02

Compound interest formula is:

$F=A{(1+\frac{c}{n})}^{nt}$,

where $F=$ future amount

$A=$ present amount
$c=$ percent interest in decimal form
$n=$ number of times compounded per year
$t=$ times in years
$A=$ present amount=$100$
$c=2\%=0.02$
$n=1$ since once per year
$t=t$

Therefore, $F=100{(1+\frac{0.02}{1})}^{1t}$

$=100{(1+0.02)}^t$

$=100{\left(1.02\right)}^t$

Hence, $x=1.02$