suppose that a loan of $5500 is given at an interest rate of 13% compounded each year. assume that no…
suppose that a loan of $5500 is given at an interest rate of 13% compounded each year. assume that no payments are made on the loan. follow the instructions below. do not do any rounding. (a) find the amount owed at the end of 1 year. $ (b) find the amount owed at the end of 2 years. $
Answer
Explanation:
Step1: Identificar la fórmula de interés compuesto
La fórmula para el interés compuesto es $A = P(1 + r)^t$, donde $A$ es el monto final, $P$ es el principal (cantidad inicial del préstamo), $r$ es la tasa de interés anual expresada como un decimal y $t$ es el número de años. Aquí, $P=$5500$, $r = 0.13$ (ya que $13%=0.13$).
Step2: Calcular el monto al final de 1 año
Sustituir $P = 5500$, $r=0.13$ y $t = 1$ en la fórmula $A = P(1 + r)^t$. $A_1=5500\times(1 + 0.13)^1=5500\times1.13 = 6215$
Step3: Calcular el monto al final de 2 años
Sustituir $P = 5500$, $r = 0.13$ y $t = 2$ en la fórmula $A = P(1 + r)^t$. $A_2=5500\times(1 + 0.13)^2=5500\times1.13^2=5500\times1.2769 = 7022.95$
Answer:
(a) $6215 (b) $7022.95