using the below formula to determine the regular payment amount. your credit card has a balance of $8900 at…

using the below formula to determine the regular payment amount. your credit card has a balance of $8900 at an annual interest rate of 22%. you decide to pay off the balance over the next 2 years. if there are no further purchases charged to the card, how much will you pay each month? show your work.\n\$p = \\frac{\\frac{r}{n}(1 + \\frac{r}{n})^{-nt}}{1-(1 + \\frac{r}{n})^{-nt}}\$

Answer

Explicación:

Paso 1: Identificar los valores dados

Tenemos $P = 8900$ (saldo del tarjeta de crédito), $r=0.22$ (tasa de interés anual), $n = 12$ (pagos mensuales, es decir, 12 periodos al año) y $t = 2$ (años).

Paso 2: Calcular la tasa de interés mensual y el número total de períodos

La tasa de interés mensual $i=\frac{r}{n}=\frac{0.22}{12}$. El número total de períodos $nt=12\times2 = 24$.

Paso 3: Sustituir valores en la fórmula

La fórmula para el pago mensual de una deuda es $M=\frac{P\times\frac{r}{n}}{1-(1 + \frac{r}{n})^{-nt}}$. Sustituyendo $P = 8900$, $\frac{r}{n}=\frac{0.22}{12}$ y $nt = 24$: [ \begin{align*} M&=\frac{8900\times\frac{0.22}{12}}{1-(1+\frac{0.22}{12})^{- 24}}\ \end{align*} ] Primero, calculamos $(1+\frac{0.22}{12})^{-24}$. Sea $x = 1+\frac{0.22}{12}\approx1 + 0.01833=1.01833$. Entonces $x^{-24}=\frac{1}{x^{24}}\approx\frac{1}{1.01833^{24}}$. Usando una calculadora, $1.01833^{24}\approx1.5697$, así que $x^{-24}\approx\frac{1}{1.5697}\approx0.637$. Luego, $8900\times\frac{0.22}{12}\approx8900\times0.01833 = 163.137$. Y $1-(1+\frac{0.22}{12})^{-24}\approx1 - 0.637=0.363$. Finalmente, $M=\frac{163.137}{0.363}\approx449.41$.

Respuesta:

$449.41$