note: please make sure to properly format your answers. all dollar figures in the answers need to include…
note: please make sure to properly format your answers. all dollar figures in the answers need to include the dollar sign and any amount over 1,000 should include the comma ($2,354.67). all percentage values in the answers need to include a percentage sign (%). for all items without specific rounding instructions, round your answers to two decimal places, show both decimal places (5.06). austin deposits $2,250 into a one - year cd at an interest rate of 2.3%, compounded daily. a. what is the ending balance after the year? round to the nearest cent. b. how much interest did the account earn during the year? c. what is the annual percentage yield? round to the nearest hundredth of a percent.
Answer
Explanation:
Step1: Definir fórmula de interés compuesto
La fórmula para el interés compuesto es $A = P(1+\frac{r}{n})^{nt}$, donde $A$ es el saldo final, $P$ es el monto inicial depositado, $r$ es la tasa de interés anual (en decimal), $n$ es el número de veces que se compone el interés por año y $t$ es el número de años. Aquí, $P = 2250$, $r=0.023$, $n = 365$ (compuesto diariamente) y $t = 1$.
Step2: Calcular el saldo final
$A=2250(1 +\frac{0.023}{365})^{365\times1}$ $A=2250(1+\frac{0.023}{365})^{365}$ $A=2250\times(1 + 0.0000630137)^{365}$ $A=2250\times1.023267$ $A\approx2302.35$
Step3: Calcular el interés ganado
El interés ganado $I$ se calcula como $I=A - P$. Sabemos que $A\approx2302.35$ y $P = 2250$, entonces $I=2302.35- 2250=52.35$.
Step4: Calcular el rendimiento anual (APY)
El rendimiento anual $APY=(1+\frac{r}{n})^{n}-1$. Sustituyendo $r = 0.023$ y $n=365$, tenemos $(1+\frac{0.023}{365})^{365}-1=(1 + 0.0000630137)^{365}-1=1.023267-1 = 0.023267\approx2.33%$
Answer:
a. $$2302.35$ b. $$52.35$ c. $2.33%$