Respuesta :
The amount in the account after six years is $15,448
Here, we want to calculate the amount that would result from compounding a deposit
To calculate this, we shall be using the compound interest formula
That would be;
[tex]\begin{gathered} A\text{ = P(1 + }\frac{r}{n})^{nt} \\ \\ \text{where A is the amount made from the compounding} \\ P\text{ is the money deposited = \$11,000} \\ r\text{ is the interest rate which is 5.7\% = }\frac{5.7}{100}\text{ = 0.057} \\ n\text{ is the number of times per year the interest is componded} \\ \sin ce\text{ it is quarterly, n= 4} \\ t\text{ is the number of years = 6 years} \end{gathered}[/tex]Substituting all these values into the equation, we have that;
[tex]\begin{gathered} A\text{ = 11,000(1 + }\frac{0.057}{4})^{4\times6} \\ \\ A=11,000(1+0.01425)^{24} \\ \\ A=11,000(1.01425)^{24} \\ \\ A\text{ = 15,448} \end{gathered}[/tex]