$765.13 is deposited at the end of each month...
$765.13 is deposited at the end of each month for 2 years in an account paying 12% interest compounded monthly. find the amount of the account. round your answer to the nearest cent. a. $18,911.18 b. $19,873.08 c. $20,638.21 d. $21,403.34 please select the best answer from the choices provided a b c d
Answer
# 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
$A=765.13\times26.9734648\approx20638.21$