Answer:
10.99%.
Step-by-step explanation:
We have been given that the Smiths bought new furniture that cost $3,298.00. The store offered them an option of putting $600 down and making equal payments of $300 a month for 10 months.
First of all, we will find amount paid by down-payments in 10 months.
[tex]\$300\times 10=\$3,000[/tex]
Total amount paid by Smiths: [tex]\$3,000+\$600=\$3,600[/tex].
Now we will find amount paid in interest by subtracting initial amount from total amount.
[tex]\text{Amount paid in interest}=\$3,600-\$3,298[/tex]
[tex]\text{Amount paid in interest}=\$302[/tex]
10 months = 10/12 year =5/6 year.
Now, we will use simple interest formula to solve for interest rate.
[tex]I=Prt[/tex]
[tex]\$302=\$3,298*r*\frac{5}{6}[/tex]
[tex]\$302=r*\frac{\$16,490}{6}[/tex]
[tex]\$302*\frac{6}{\$16,490}=r*\frac{\$16,490}{6}*\frac{6}{\$16,490}[/tex]
[tex]\frac{1,812}{\$16,490}=r[/tex]
[tex]r=\frac{1,812}{\$16,490}[/tex]
[tex]r=0.1098847786[/tex]
[tex]r=0.1098847786\times 100[/tex]
[tex]r=10.98847786\%[/tex]
[tex]r\approx 10.99\%[/tex]
Therefore, the annual interest rate is 10.99%.
