Joaquin has agreed to lend his younger brother $$45$ so that he can buy a new tank for his pet lizard.

1. Joaquin is charging his brother $2\%$ simple interest per month. If his brother pays him back in 6 months, how much will Joaquin get back?

   Hint (a):

   Using the equation for simple interest:

   $\text{Interest} = Prt$
   $P = \text{principal}$
   $r = \text{interest rate}$
   $t = \text{time}$

   More Help (a):

   $\text{Interest} = $45(.02)(6 \text{ months})$

   Answer (a):

   $$50.40$

   Remember, the total money Joaquin gets back includes the principal and the interest.

2. If Joaquin’s brother instead borrowed the money from a bank at $2\%$ compound interest per month, how much would he have to pay the bank at the end of 6 months?

   Hint (b):

   Use the equation for compound interest:
   
   $\text{Total Amount} = P(1 + r)^{n}$
   $P = \text{principal}$
   $r = \text{rate}$
   $n = \text{number of times compounded}$

   Answer (b):

   $$45(1+.02)^6=$45\cdot 1.02^6=$50.68$