$765.13 is deposited at the end of each month for 2 years in an account paying 12% interest compounded…

Answer:

C. $20,638.21

Explanation:

Step1: Identificar los valores

$P = 765.13$, $r=0.12$, $n = 12$, $t = 2$

Step2: Calcular la tasa mensual y el número de períodos

$i=\frac{r}{n}=\frac{0.12}{12}=0.01$ $m = n\times t=12\times2 = 24$

Step3: Aplicar la fórmula de la serie de pagos

$A=P\times\frac{(1 + i)^{m}-1}{i}$ $A = 765.13\times\frac{(1 + 0.01)^{24}-1}{0.01}$

Step4: Calcular $(1 + 0.01)^{24}$

$(1 + 0.01)^{24}\approx1.269734648$

Step5: Calcular el numerador

$(1 + 0.01)^{24}-1\approx1.269734648 - 1=0.269734648$

Step6: Calcular el cociente

$\frac{(1 + 0.01)^{24}-1}{0.01}\approx\frac{0.269734648}{0.01}=26.9734648$

Step7: Calcular el monto final

$A=765.13\times26.9734648\approx20638.21$