a furniture store offers a one - year monthly installment plan for a set of living room furniture. the…

a furniture store offers a one - year monthly installment plan for a set of living room furniture. the payment for the first month is $65, and then it increases by 5% each month for the rest of the year. how much money is paid after 12 months? round your answer to the nearest dollar.\n$780\n$819\n$1,035\n$1,401

a furniture store offers a one - year monthly installment plan for a set of living room furniture. the payment for the first month is $65, and then it increases by 5% each month for the rest of the year. how much money is paid after 12 months? round your answer to the nearest dollar.\n$780\n$819\n$1,035\n$1,401

Answer

Answer:

C. $1,035

Explanation:

Step1: Identificar la serie geométrica

Tenemos una serie geométrica donde $a_1 = 65$ (pago del primer mes) y $r=1 + 0.05=1.05$ (factor de crecimiento mensual). La fórmula para la suma de los primeros $n$ términos de una serie geométrica es $S_n=\frac{a_1(1 - r^n)}{1 - r}$ cuando $r\neq1$, y $n = 12$ (número de meses).

Step2: Sustituir valores en la fórmula

Sustituimos $a_1 = 65$, $r = 1.05$ y $n = 12$ en la fórmula $S_{12}=\frac{65(1 - 1.05^{12})}{1 - 1.05}$.

Step3: Calcular $1.05^{12}$

$1.05^{12}\approx1.795856$.

Step4: Calcular el numerador

$1-1.05^{12}=1 - 1.795856=- 0.795856$, y $65\times(-0.795856)=-51.73064$.

Step5: Calcular el denominador

$1 - 1.05=-0.05$.

Step6: Calcular la suma

$S_{12}=\frac{-51.73064}{-0.05}=1034.6128\approx1035$.