Question

The Smiths bought new furniture that cost $3,298.00. The store offered them

Answer 1

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.

$\ 300\times 10=\ 3,000$

Total amount paid by Smiths: $\ 3,000+\ 600=\ 3,600$.

Now we will find amount paid in interest by subtracting initial amount from total amount.

$\text{Amount paid in interest}=\ 3,600-\ 3,298$

$\text{Amount paid in interest}=\ 302$

10 months = 10/12 year =5/6 year.

Now, we will use simple interest formula to solve for interest rate.

$I=Prt$

$\ 302=\ 3,298*r*\frac{5}{6}$

$\ 302=r*\frac{\ 16,490}{6}$

$\ 302*\frac{6}{\ 16,490}=r*\frac{\ 16,490}{6}*\frac{6}{\ 16,490}$

$\frac{1,812}{\ 16,490}=r$

$r=\frac{1,812}{\ 16,490}$

$r=0.1098847786$

$r=0.1098847786\times 100$

$r=10.98847786\%$

$r\approx 10.99\%$

Therefore, the annual interest rate is 10.99%.