Modern Appliances offers a one-year monthly installment plan for a refrigerator. The payment for the first month is $75, and then it increases by 6% each month for the rest of the year. Which expression can be used to find the total paid in the first 12 months?

Expression used represents the given paid installment for [tex]12[/tex] months is equal to [tex]S_{12} =\frac{ 75(1-1.06^{12}) }{1-1.06}[/tex].

What is expression?

" Expression is defined as the equation representing the relation between the numbers or the variables using mathematical operation."

Formula used

Geometric progression,

[tex]S_{n} = \frac{a(1-r^{n}) }{1-r}[/tex]

[tex]a=[/tex] first term

[tex]r=[/tex] common ratio

[tex]n=[/tex] number of terms

According to the question,

Given,

Amount to be paid first month [tex]'a' = \$75[/tex]

Increases by [tex]6\%[/tex] each month

Therefore,

Common ratio [tex]'r' = 1 + \frac{6}{100}[/tex]

[tex]= 1.06[/tex]

Number of months [tex]'n'= 12[/tex]

Substitute the value in the formula to get the expression for the given condition,

Required expression,

[tex]S_{12} =\frac{ 75(1-1.06^{12}) }{1-1.06}[/tex]

Hence, expression used represents the given paid installment for [tex]12[/tex] months is equal to [tex]S_{12} =\frac{ 75(1-1.06^{12}) }{1-1.06}[/tex].

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