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 (5.06). how much more would $10,000 earn in three years compounded daily at 1.33% than compounded semi - annually at 1.33%?
Answer
Explanation:
Step1: Fórmula de interés compuesto
La fórmula de interés compuesto es $A = P(1+\frac{r}{n})^{nt}$, donde $P$ es el principal ($P = 10000$), $r$ es la tasa de interés anual (en decimal, $r = 0.0133$), $n$ es el número de veces que se capitaliza el interés por año y $t$ es el número de años ($t = 3$).
Caso 1: Capitalización diaria
Para la capitalización diaria, $n = 365$. Entonces $A_1=10000(1 +\frac{0.0133}{365})^{365\times3}$. Calculamos $(1+\frac{0.0133}{365})^{365\times3}=(1+\frac{0.0133}{365})^{1095}$. $1+\frac{0.0133}{365}\approx1 + 0.0000364384 = 1.0000364384$. $(1.0000364384)^{1095}\approx1.04077$. $A_1 = 10000\times1.04077=10407.70$.
Caso 2: Capitalización semianual
Para la capitalización semianual, $n = 2$. Entonces $A_2=10000(1+\frac{0.0133}{2})^{2\times3}$. Calculamos $1+\frac{0.0133}{2}=1 + 0.00665 = 1.00665$. $(1.00665)^{6}\approx1.04046$. $A_2 = 10000\times1.04046 = 10404.60$.
Step2: Diferencia entre los dos casos
Calculamos la diferencia $D=A_1 - A_2$. $D = 10407.70-10404.60 = 3.10$.
Answer:
$3.10$