Modern Electronics offers a one-year monthly installment plan for a big screen TV. The payment for the first month is 62 dollars , and then it increases by 4 percent each month for the rest of the year. Which expression can be used to find the total amount paid in the first 12 months?
Answer
A
62 times open paren the fraction with numerator 1 minus 1 point 0 4 raised to the 0 point 0 4 power and denominator 1 minus 12 close paren
B
62 times open paren the fraction with numerator 1 minus 1 point 0 4 to the 12th power and denominator 1 minus 0 point 0 4 close paren
C
62 times open paren the fraction with numerator 1 minus 1 point 0 4 to the 12th power and denominator 1 minus 1 point 0 4 close paren
D
62 times open paren the fraction with numerator 1 minus 0 point 0 4 to the 12th power and denominator 1 minus 0 point 0 4 close paren
Explanation
The monthly payments form a geometric sequence: the first payment is $62, and each payment is 1.04 times the previous one. The total for 12 payments is the geometric-series sum, 62(1 − 1.04^12)/(1 − 1.04). This matches the expression in choice C.
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