Studdy AI Logo
Math  /  Algebra

QuestionExam instructions
Question 2 of 20 : equivalent to what actual yearly rate of interest? A. 25\% B. 67%67 \% C. 65%65 \% D. 85%85 \% Mark for review (Will be highlighted on the review page) ex Previous Ouestion Next Ouestion >> Bevera My A

Studdy Solution

STEP 1

1. Sarah bought a lawnmower for 320.<br/>2.Shepaid320.<br />2. She paid 100 down and will pay $25 for 12 months.
3. We need to find the equivalent actual yearly rate of interest.
4. The options for the equivalent interest rate are 25%, 67%, 65%, and 85%.

STEP 2

1. Calculate the total amount paid.
2. Determine the total interest paid.
3. Calculate the equivalent yearly interest rate.

STEP 3

Calculate the total amount paid by Sarah.
The down payment is 100,andshemakes12monthlypaymentsof100, and she makes 12 monthly payments of 25 each. Therefore, the total amount paid is:
Total Amount Paid=100+(25×12) \text{Total Amount Paid} = 100 + (25 \times 12)
Total Amount Paid=100+300 \text{Total Amount Paid} = 100 + 300
Total Amount Paid=400 \text{Total Amount Paid} = 400

STEP 4

Determine the total interest paid.
The original price of the lawnmower is 320,andthetotalamountpaidis320, and the total amount paid is 400. Therefore, the total interest paid is:
Total Interest Paid=400−320 \text{Total Interest Paid} = 400 - 320
Total Interest Paid=80 \text{Total Interest Paid} = 80

STEP 5

Calculate the equivalent yearly interest rate.
The interest paid is 80onaprincipalof80 on a principal of 320. To find the equivalent yearly interest rate, we use the formula for simple interest:
Interest Rate=(Total Interest PaidPrincipal)×100% \text{Interest Rate} = \left( \frac{\text{Total Interest Paid}}{\text{Principal}} \right) \times 100\%
Interest Rate=(80320)×100% \text{Interest Rate} = \left( \frac{80}{320} \right) \times 100\%
Interest Rate=0.25×100% \text{Interest Rate} = 0.25 \times 100\%
Interest Rate=25% \text{Interest Rate} = 25\%
The equivalent actual yearly rate of interest is:
25% \boxed{25\%}

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord