To solve this problem, let's break it down step by step:
1. Determine the total cost paid through the installment plan:
- Sarah made a down payment of [tex]$100.
- Then, she made monthly payments of $[/tex]25 for 12 months.
- The total amount paid per month for 12 months is [tex]\( 25 \times 12 = 300 \)[/tex].
- Adding the down payment, the total cost paid by Sarah is [tex]\( 100 + 300 = 400 \)[/tex].
2. Calculate the extra cost paid by taking the installment plan:
- The original purchase price of the lawnmower was [tex]$320.
- The total payments made through the installment plan is $[/tex]400.
- The extra cost paid due to the installment plan is [tex]\( 400 - 320 = 80 \)[/tex].
3. Calculate the effective principal being financed:
- The principal amount is the purchase price minus the down payment.
- So, the principal financed amount is [tex]\( 320 - 100 = 220 \)[/tex].
4. Determine the yearly rate of interest:
- We know the extra cost paid ($80) can be treated as the interest on the principal amount.
- Interest = Principal Rate Time
- Rearranging this to find the rate gives us Rate = (Interest / Principal).
- Our time period is 1 year.
Plugging in the values:
[tex]\[
\text{Rate} = \left(\frac{\text{Extra Cost}}{\text{Principal}}\right) \times 100
\][/tex]
[tex]\[
\text{Rate} = \left(\frac{80}{220}\right) \times 100 \approx 36.36\%
\][/tex]
So, the actual yearly rate of interest that corresponds to the extra cost paid by taking this plan is approximately [tex]\( 36.36\% \)[/tex].
Since none of the provided options match 36.36%, it seems there may be an error in the given options. Therefore, there is no choice that represents the correct yearly rate of interest of around [tex]\( 36.36\% \)[/tex].
