Respuesta :
[tex]\begin{gathered} a)\text{ Balance = \$4804.87} \\ \text{Interest = \$604.87} \\ \\ b)\text{Balance = \$}4798.46 \\ \text{Interest = \$}598.46 \\ \\ c)\text{ Balance = \$4767} \\ Interest\text{ = \$567} \end{gathered}[/tex]Explanation:
a) Principal = $4200
rate = 2.7% = 0.027
time = 5 years
Balance = ?
n = 4 (quarterly)
Using compund interest formula:
[tex]FV\text{ = P(1 +}\frac{r}{n})^{nt}[/tex][tex]\begin{gathered} FV\text{ = balance} \\ \text{Balance = 4200(1 + }\frac{0.027}{4})^{4\times5} \\ \text{Balance = 4200(1 + }0.00675)^{20} \\ \text{Balance = 4804.87} \\ \\ \text{Interest = Balance - principal} \\ \text{Interest = \$4804.87 - \$4200} \\ \text{Interest = \$604.87} \end{gathered}[/tex]For annual compounding, n = 1
[tex]\begin{gathered} FV\text{ = balance} \\ \text{Balance = 4200(1 + }\frac{0.027}{1})^{1\times5} \\ \text{Balance = 4200(1 + }0.027)^5 \\ \text{Balance = \$ }4798.46 \\ \\ \text{Interest = Balance - principal} \\ \text{Interest = \$}4798.46\text{ - \$4200} \\ \text{Interest = \$}598.46 \end{gathered}[/tex]Using simple interest:
[tex]\begin{gathered} I\text{ = PRT} \\ I\text{ = interest, P = principal, R = rate, T = time} \\ I\text{ = }4200\times0.027\times5 \\ Interest\text{ = \$567} \\ \\ \text{Balance = Principal + Interest} \\ \text{Balance = 4200 + 567} \\ \text{Balance = \$4767} \end{gathered}[/tex]