Write an expression for each of the following situations. You do not need to calculate the values, just write the expressions.

1. How much money will you have after $5$ years if $$1050$ is invested at $7\%$ annual interest, compounded quarterly?

   Step (a):

   $1050\left(1+\frac{0.07}{4}\right)^{4\cdot5}$

2. How much money will you have after $10$ years if $$5000$ is invested at $8.2%$ annual interest, compounded monthly?

   Step (b):

   $5000 \left( 1+\frac{0.082}{12} \right)^ {120}$

3. How much money will you have after $t$ years if $P$ dollars are invested at $r\%$ annual interest, compounded $n$ times per year?

   Hint (c):

   $1. \ \ P\text{ is the initial amount.}$

   $2. \ \ 1 + \frac{r}{100n}\text{ is the multiplier.}$

   $3.\ \ nt \text{ is the number of times it will be compounded.}$