​Use your knowledge of compound interest to complete the parts below.  

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

   Step (a):

   $1050\left(1+\frac{0.07}{4}\right)^{(4)(5)}$ 

2. How long will it take an account to have $\$11,000$ if $\$5000$ is invested at $8.2\%$ annual interest, compounded monthly?

   Step (b):

   $5000 \left( 1+\frac{0.082}{12} \right)^ {(10)(12)}$ 

3. Write an equation for the amount of money you will have after $t$ years if $P$ dollars are invested at $r\%$ annual interest, compounded $n$ times per year.

   Hint (c):

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

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

   $3.\ \ nt \text{ is the number of compoundings.}$