Question

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 1

We will apply the compound interest formula

`\begin{gathered} A=P(1+(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 = }(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}`

Substituting the values into the equation we have

`\begin{gathered} A=P(1+(r)/(n))^(nt) \\ A=6000(1+(0.031)/(4))^(4*4) \\ A=6000(1+0.00775)^(16) \\ A=6000(1.00775)^(16) \\ A=6000*1.1314748 \\ A=6788.84916 \end{gathered}`

Hence the answer is $6788.85