Question

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

Write a function that gives the total value V(t) in dollars, of the investment t years from now.

Answer 1

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

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 + (r)/(100)`. So, after year
`1` we will have
`S_(1) = S + (r)/(100)S = S(1 + (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 + (r)/(100) = 1 + (2)/(100) = (100)/(100) + (2)/(100) = (102)/(100) = 1,02`. Therefore,
`V(t) = Sp^t = 2 * 10^3 * 1,02^t`.