Question

Shota invests $2000 in a certificate of deposit that earns 2%, percent in interest each year.

Answer 1

Answer:

$2 * 10^3 * 1,02^t$

Step-by-step explanation:

Let $S = 2000 = 2 * 10^3$ dollars be our investment, $r = 2\%$ - our interest rate. In order to simplify things, I suggest bringing the variable $p$ into play: $p = 1 + \frac{r}{100}$. So, after year $1$ we will have $S_{1} = S + \frac{r}{100}S = S(1 + \frac{r}{100} ) = Sp$. After year $2$: $S_{2} = S_{1}p = Sp * p = Sp^2$. After year $t$: $S_{t} = S_{t - 1}p = Sp^t$. Besides, we can count $p$. Indeed, $p = 1 + \frac{r}{100} = 1 + \frac{2}{100} = \frac{100}{100} + \frac{2}{100} = \frac{102}{100} = 1,02$. Therefore, $V(t) = Sp^t = 2 * 10^3 * 1,02^t$.