tristan invested $1,300 in an account paying an interest rate of 6.1% compounded monthly. assuming no…

tristan invested $1,300 in an account paying an interest rate of 6.1% compounded monthly. assuming no deposits or withdrawals are made, how much money, to the nearest ten dollars, would be in the account after 6 years?

tristan invested $1,300 in an account paying an interest rate of 6.1% compounded monthly. assuming no deposits or withdrawals are made, how much money, to the nearest ten dollars, would be in the account after 6 years?

Answer

Explanation:

Step1: Identificar la fórmula de interés compuesto

La fórmula para el interés compuesto es ( A = P(1+\frac{r}{n})^{nt} ), donde ( P ) es el principal (( P = 1300 )), ( r ) es la tasa de interés anual ( ( r=0.061 )), ( n ) es el número de veces que se compone el interés por año ( ( n = 12 ) ya que es mensual), y ( t ) es el número de años ( ( t=6 )).

Step2: Sustituir los valores en la fórmula

Sustituimos los valores: ( A = 1300(1+\frac{0.061}{12})^{12\times6} ). Primero calculamos ( \frac{0.061}{12}\approx0.005083 ), luego ( 1 + 0.005083=1.005083 ), y ( 12\times6 = 72 ). Entonces ( A = 1300\times(1.005083)^{72} ).

Step3: Calcular ( (1.005083)^{72} )

Calculando ( (1.005083)^{72}\approx1.4449 ).

Step4: Calcular ( A )

Multiplicamos ( 1300\times1.4449 = 1878.37\approx1880 ) (redondeado al decena de dólares más cercana).

Answer:

( 1880 )