What is the effective annual interest rate on a 9% APR automobile loan that has monthly payments?Question 2

To calculate the effective annual interest rate, we need to take into account the compounding period, which in this case is monthly.

Here are the steps:

1. First, divide the annual interest rate (in decimal form, so 9% becomes 0.09) by the number of compounding periods per year. In this case, there are 12 months in a year, so we have 0.09/12 = 0.0075. This is the monthly interest rate.

2. Next, add 1 to this rate: 1 + 0.0075 = 1.0075.

3. Then, raise this sum to the power of the number of compounding periods per year: (1.0075)^12 ≈ 1.093806.

4. Subtract 1 from this result to find the effective annual rate: 1.093806 - 1 = 0.093806 or 9.38%.

So, the effective annual interest rate for a 9% APR automobile loan with monthly payments is approximately 9.38%.

Para calcular la tasa de interés anual efectiva (EAR) de un préstamo de automóvil con una Tasa de Porcentaje Anual (APR) del 9% y pagos mensuales, sigue estos pasos:

1. Convertir la APR a una tasa de interés mensual: La APR del 9% es una tasa anual, por lo que primero debemos convertirla a una tasa mensual. Dividimos la APR por 12 (el número de meses en un año).

   $\text{Tasa de interés mensual} = \frac{9\%}{12} = 0.75\%$

2. Convertir la tasa de interés mensual a un decimal: Para los cálculos, es más fácil trabajar con decimales. Convertimos el 0.75% a un decimal dividiéndolo por 100.

   [ \text{Tasa de interés mensual en decimal} = \frac{0