Question

shota invests $2000 in a certificate of deposit that earns 2% in interest each year. write a function that gives the total value v(t), in dollars, of the investment t years from now. do not enter commas in your answer. v(t) =

Explanation:

Step1: Identify compound interest formula

This is annual compound interest, so the formula is $V(t) = P(1+r)^t$, where $P$ is principal, $r$ is annual interest rate, $t$ is time in years.

Step2: Substitute given values

$P=2000$, $r=0.02$ (2% converted to decimal). Substitute into the formula:
$V(t) = 2000(1+0.02)^t$

Step3: Simplify the growth factor

Simplify $1+0.02$ to $1.02$:
$V(t) = 2000(1.02)^t$

Answer:

$V(t)=2000(1.02)^t$