1. **State the problem:** Jersey wants to buy a guitar with a 15% down payment and pay the remainder plus a finance charge in monthly installments over 2 years. The monthly payment is 88.75. We need to find the finance charge. 2. **Define variables:** Let the total price of the guitar be $P$. 3. **Calculate down payment:** The down payment is 15% of $P$, so down payment = $0.15P$. 4. **Calculate amount financed:** The amount financed (principal) is the remainder after down payment, which is $0.85P$. 5. **Calculate total amount paid in installments:** Monthly payment is 88.75 for 2 years (24 months), so total paid = $88.75 \times 24 = 2130$. 6. **Calculate finance charge:** Finance charge = total paid in installments - amount financed = $2130 - 0.85P$. 7. **Find $P$ using the fact that total paid in installments includes principal and finance charge:** Since the financed amount plus finance charge equals total paid, and financed amount is $0.85P$, we have: $$2130 = 0.85P + \text{finance charge}$$ But we need to find finance charge, so we need $P$ first. 8. **Use the fact that the down payment plus financed amount equals total price:** $$P = 0.15P + 0.85P$$ This is true by definition. 9. **Express finance charge in terms of $P$ and solve for $P$ using the monthly payment:** Since the monthly payment is fixed, the financed amount plus finance charge equals $2130$. We can write: $$\text{finance charge} = 2130 - 0.85P$$ But we need to find $P$ to find finance charge. 10. **Assuming the problem implies the financed amount is $0.85P$ and the monthly payment covers principal plus finance charge, we can find $P$ by considering the total cost including down payment and installments:** Total cost = down payment + total installments = $0.15P + 2130$ But total cost is also $P + \text{finance charge}$. Since finance charge is included in the installments, total cost = $P + \text{finance charge}$. From step 6, finance charge = $2130 - 0.85P$. So total cost = $P + 2130 - 0.85P = 0.15P + 2130$. This matches the total cost from down payment plus installments, confirming consistency. 11. **To find finance charge, we need $P$. Use the monthly payment to find $P$ by noting that the financed amount is $0.85P$ and the monthly payment is $88.75$ over 24 months:** $$\text{Monthly payment} = \frac{\text{financed amount} + \text{finance charge}}{24} = 88.75$$ But financed amount + finance charge = $2130$ (from step 5), so this is consistent. 12. **Since we cannot find $P$ directly from given data, assume the financed amount is $0.85P$ and the total paid in installments is $2130$, so finance charge = $2130 - 0.85P$. If we assume the financed amount is the principal only, then the finance charge is the difference between total paid and principal. 13. **To find $P$, use the fact that the down payment is 15% of $P$, so down payment = $0.15P$. The total cost is down payment plus total installments = $0.15P + 2130$. But total cost is $P + \text{finance charge}$. From step 6, finance charge = $2130 - 0.85P$. So total cost = $P + 2130 - 0.85P = 0.15P + 2130$. This confirms the total cost is consistent. 14. **Since the problem asks for the finance charge, and we know the financed amount is $0.85P$, and total installments paid is $2130$, finance charge = $2130 - 0.85P$. 15. **To find $P$, use the fact that the monthly payment is $88.75$ for 24 months, so total installments = $2130$. Assuming the financed amount is $0.85P$, and the finance charge is the difference, we can solve for $P$: $$\text{finance charge} = 2130 - 0.85P$$ But we need $P$ to find finance charge. 16. **Since the problem does not provide the total price $P$, we cannot find the exact finance charge without $P$. However, if the problem implies the financed amount is the principal, then the finance charge is the difference between total installments and the financed amount.** 17. **Therefore, the finance charge is:** $$\boxed{\text{finance charge} = 2130 - 0.85P}$$ Without the total price $P$, the finance charge cannot be numerically determined. **Summary:** The finance charge equals the total amount paid in installments minus the financed amount (85% of the guitar price). Without the guitar price, the exact finance charge cannot be calculated.