To determine the equivalent yearly interest rate for Sarah's buy now, pay later plan, let's carefully go through the steps and interpret the given results.
1. Understanding the Initial Cost and Payments:
- Sarah bought a lawnmower for [tex]$8320.
- She made an initial down payment of $[/tex]100.
- She agreed to pay [tex]$25 per month for the next 12 months.
2. Calculate the Total Amount Paid Over the Year:
- Initial down payment: $[/tex]100
- Monthly payments: [tex]$25/month for 12 months, which totals $[/tex]25 * 12 = [tex]$300.
- Therefore, the total amount paid over one year is $[/tex]100 (down payment) + [tex]$300 (monthly payments) = $[/tex]400.
3. Extra Cost Paid:
- The actual cost of the lawnmower was [tex]$8320.
- The total amount paid over the year is $[/tex]400.
- The extra cost paid by Sarah is [tex]$400 - $[/tex]8320 = -[tex]$7920 (indicating no extra cost; actually, it looks like a saving if interpreted mathematically, which is uncommon in real terms).
4. Calculate the Principal Amount Financed:
- Principal amount Sarah financed (excluding the down payment): $[/tex]8320 - [tex]$100 = $[/tex]8220.
5. Determine the Effective Yearly Interest Rate:
- The formula for the equivalent yearly interest rate is: [tex]\[
\text{Rate} = \left(\frac{\text{Extra Cost}}{\text{Principal}}\right) \times \left(\frac{12}{\text{Number of Months Paid}}\right) \times 100
\][/tex]
- Substituting the values in:
[tex]\[
\text{Rate} = \left(\frac{-7920}{8220}\right) \times \left(\frac{12}{12}\right) \times 100
\][/tex]
- This simplifies to:
[tex]\[
\text{Rate} = -0.9635036496350365 \times 100
\][/tex]
- Therefore, the effective yearly interest rate: [tex]\[
\text{Rate} = -96.35\%
\][/tex]
Given the calculated interest rate, Sarah is finding a highly unusual effective interest rate of approximately -96.35%. This negative rate typically implies an atypical financial scenario. Considering it suggests a mistake in conventional contexts, it's best to understand the fictional nature here, highlighting that standard interpretations in practical scenarios are generally positive rates.
Given the options:
A. 8 कै (irrelevant option)
B. [tex]$25 \%$[/tex]
C. [tex]$6 / \%$[/tex] (irrelevant option)
D. [tex]$65 \%$[/tex]
None of the listed options seemingly match the exact -96.35%. The answers provided in the options may not correctly reflect this unusual scenario designed. Conventionally, positive rates above interest suggest a misalignment in options supplied for interpretative understanding exploration of theoretical scenarios, not standard financial calculations.
