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Question content area topPart 1Use the periodic compound interest formula to solve.Suppose that$6000 is invested at3.1% compoundedquarterly. Find the total amount of this investment after4 years.Part 1The amount after4 years will be $enter your response here

Answer :

SOLUTION

We will apply the compound interest formula

[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \text{Where } \\ A=\text{ amount aft}er\text{ 4 years }=\text{?} \\ P=\text{ principal, that is money invested = }6000\text{ dollars } \\ r=\text{ interest rate = }\frac{3.1}{100}=0.031 \\ n=n\text{umber of times compounding, that is quarterly = 4} \\ t\text{ = time in years = 4 years } \end{gathered}[/tex]

Substituting the values into the equation we have

[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ A=6000(1+\frac{0.031}{4})^{4\times4} \\ A=6000(1+0.00775)^{16} \\ A=6000(1.00775)^{16} \\ A=6000\times1.1314748 \\ A=6788.84916 \end{gathered}[/tex]

Hence the answer is $6788.85