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.

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

Explicación:

Paso 1: 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 ($P = 2250$), $r$ es la tasa de interés anual en decimal ($r=0.023$), $n$ es el número de veces que se compone el interés por año ($n = 365$ para diario) y $t$ es el número de años ($t = 1$).

Paso 2: Calcular el saldo final (a)

Sustituir los valores en la fórmula: $A=2250(1 +\frac{0.023}{365})^{365\times1}$ $A=2250(1+\frac{0.023}{365})^{365}$ $A=2250(1 + 0.0000630137)^{365}$ $A=2250(1.0000630137)^{365}$ $A=2250\times1.023267$ $A=$2250\times1.023267=$2302.35$

Paso 3: Calcular el interés ganado (b)

El interés $I$ es $I=A - P$. $I = 2302.35- 2250=$52.35$

Paso 4: Calcular el rendimiento anual (c)

El rendimiento anual (APY) se calcula con la fórmula $APY=(1+\frac{r}{n})^{n}-1$. $APY=(1+\frac{0.023}{365})^{365}-1$ $APY=(1.0000630137)^{365}-1$ $APY = 1.023267-1$ $APY=0.023267$ Expresado como porcentaje y redondeado: $APY = 2.33%$

Respuesta:

a. $$2302.35$ b. $$52.35$ c. $2.33%$