Show how you get the answer step by step i dont know the process i need to know how to do it i will medal charlotte purchased a pool for $7680 using a six-month deferred payment plan with an interest rate of 20.45%. she did not make any payments during the deferment period. what will charlotte's monthly payment be if she must pay off the pool within three years after the deferment period?

Initially, Charlotte owes $7680. She finishes her payments after a total of 6 + 36 = 42 months. Using a simple compounding formula, the amount she owes is worth P at the end of 42 months, where P is: 
  P = 7680 * (1 + .2045/12)^42 = 15616.67379
  Now, the first installment she pays (at the end of six months) is paid 35 months in advance of the end, so it is worth x * (1 + .2375/12)^35 at the end of her loan period. 
  Similarly, the second installment is worth x * (1 + .2375/12)^34 at the end of the loan period. 
  Continuing, this way, the last installment is worth exactly x at the end of the loan period. 
  So, the total amount she paid equals: 
  x [(1 + .2375/12)^35 + (1 + .2375/12)^34 + ... + (1 + .2375/12)^0] 
  To calculate this, assume that 1+.2045/12 = a. Then the amount Charlotte pays is: 
  x (a^35 + a^34 + ... + a^0) = x (a^36 - 1)/(a - 1) 
  Clearly, this value must equal P, so we have: 
  x (a^36 - 1)/(a - 1) = P = 15616.67379
  Substituting, a = 1 + .2045/12 and solving, we get 
  x = 317.82

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