Respuesta :
Account 1 because it earns about $10 more than Account 2
Explanation
to solve this we can find the amounts and then compare them, so
Step 1
Account 1 requires an investment of $700 and earns 6.2% interest, compounded quarterly
so
to find the future value we need apply the formula
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ where \\ A\text{ is the amount ( future value)} \\ P\text{ =Principal ( initial amount)} \\ r=\text{interest rate} \\ n=\nu mber\text{ of compounded times in one "t"} \\ t=time \end{gathered}[/tex]then, let
[tex]\begin{gathered} A=\text{unknown} \\ P\text{ =7}00 \\ r=\text{6}.2\text{ \% = 0.062} \\ n=4(\text{ it is quartelyr)} \\ t=3\text{ years} \end{gathered}[/tex]replace and evaluate
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ A=700(1+\frac{0.062}{4})^{4\cdot3} \\ A=700(1.0155)^{12} \\ A=841.89 \end{gathered}[/tex]it means that for account 1, the earning is
[tex]\begin{gathered} \text{Earning}=\text{ actual-initial } \\ \text{Earning}=841.89-700=141.89 \end{gathered}[/tex]account 1: 141.89
Step 2
now, for account 2
Account 2 requires an investment of $800 and earns 5.1% interest, compounded monthly.
Let
[tex]\begin{gathered} A=\text{unknown} \\ P\text{ =8}00 \\ r=\text{5}.1\text{ \% = 0.05}1 \\ n=12(monthly\text{)} \\ t=3\text{ years} \end{gathered}[/tex]replace and evaluate
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ A=800(1+\frac{0.051}{12})^{12\cdot3} \\ A=800(1.00425)^{36} \\ A=800(1.164) \\ A=931.957 \end{gathered}[/tex]so, the earnings in option2 would be:
[tex]\begin{gathered} \text{Earning}=\text{ actual-initial } \\ \text{Earning}=931.957-800=131.96 \end{gathered}[/tex]Step 3
finally, let's compare the earnings
[tex]\begin{gathered} \text{Option 1 :141.89} \\ \text{Option 2: 131.96} \\ \text{Option 1 -option 2=141.89-131.96}\approx10 \\ so,\text{ difference is about 10} \\ \text{account 1 is 10 more than account 2} \end{gathered}[/tex]therefore, the answer is
Account 1 because it earns about $10 more than Account 2
I hope this helps you
